Great to see that I am not the only one in the world who care about this issue with the a6300 :-) And thanks for sharing what you have found out.
The missing headhone jack is the biggest drawback of the a6300 for anyone trying to use it for documentary work etc.
I have researched the web for a solution to this problem ever since the a6300 was announced and have come to most of the same conclusions as you have.
I found out about the Shure VP83F which is nice if you only have to record the shotgun itself. But sadly they did not include an input to also record/monitor an external source on that one. I was hoping that you could unplug the shotgun from the recording unit, but found out that you probably cant do that. I have to always be able to record and monitor two sources for my work (not neccesarily at the same time). At least one wireless receiver (for wireless reporter handmic, wireless lapel mic interview, actor etc) and one mini shotgun or some mic that would record just general ambience. So I gave up on this mic.
Rode at one point announced a version of their videomic pro that had a built in recorder
This also had an input for an external mic. And probably a headphone output. This would have been an incredible solution not only for the a6300 but for the many panasonic/canon cameras that lack the same. But sadly they never released it, and I guess they probably never will.
There is also this thing that I bought:
Some of the older Sennheiser wireless receivers have headphone output (with nice seperate easily adjustable volume). This is what I have been using with my a6300 and it works great. The preamps in the a6300 are very good. They remind me of the ones in my a7s. And with the very hot signal from the Sennheiser you could turn down the input volume on the a6300 to get even better sound. The problem is that I have to constantly remove the mic input cable from the a6300 whenever I want to use the built in mics of the camera to record ambience when I dont use the wireless system. I am afraid that I will sooner or later forget to put the cable back in for an interview and not record the audio from the wireless receiver but from the built in camera mics. This is the biggest drawback about monitoring the audio outside of the camera. You can never be sure that what it records is what you are monitoring. For now I am able to live with this solution but have to be very careful to not make a mistake. But soon the older Sennheisers will have to be replaced and then there will be no headphone output.
I have tried the zoom h1 as a solution. But the problem with this is like you point out. It does not have a seperate headphone output. So you would have to use a sescom splitter cable to be able to split the signal into one cable with a "mic level" signal for the camera and one with a "headphone level" for monitoring. One of the problems with this is that you cant control the two levels seperatly. Which could become a pain because you can get a too loud or too weak volume depending on your headphones or preference. Headphones with a volume control or a headphone amplifer could solve this but it starts to become a mess of cables and boxes.
The other problem with the zoom h1 is that its included mic do not have any sort of shock protection. So even the slightest movement you do with the camera will be recorded. The h1 is also unable to record/mix a different source to left/right channel.
The Zoom H5 is more ideal for this purpose. This is (as far as I have found out) the only external recorder (at a reasonable size) that has a seperate headphone output (adjustable level with seperate button) along with an output for the camera (adjustable mix/line level with seperate button etc).
The included microphone has some sort of rubber shock mount. It can absolutely not compare to a real shouck mount like the one on the Rode Videomic Pro. But it works well enough that if you are careful you can handhold the camera and record OK ambience with this so you wount need a seperate shotgun mic to do this.
The h5 has two modes. A stereo mode and a multi channel mode. In stereo mode you can quickly (just a press of a button) change between its built in stereo mic and external sources (the two XLR inputs, one goes to the left channel the other to the right). In multi channel mode you can mix down the inputs so you can put the built in mic to the right channel, and en external source to the left channel to achieve the same as a pro-camcorder does with its two sound inputs. If you record to the Zoom itself along with on the camera you will be able to add stereo sound from the built in mics etc in post production since it records all inputs to seperate files.
The output level/impedance of the zoom to the camera can be adjusted so you can find a level that suits the a7s or the a6300 with no problem.
With the new super small Sennheiser wireless system that have small XLR shaped receivers this could become a very compact system even with two wireless receivers.
The drawbacks to the Zoom h5 is:
-it is kind of big, but not as big as it looks in the pictures. If you remove the mic module it will be an OK size but I hope they one day make a smaller version.
-the problem is that it does not have a seperate 3.5mm input with mic power on the recorder itself. This input is on the mic module so you cant remove this even if you want to add a seperate shotgun mic that uses a 3.5mm cable. An adapter for XLR might solve this.
-It would be nice if zoom released a mini shotgun module (there is a laaaarge one) with real shock mount for it.
I have consideres the adapter solution (HDMI) that you have tried. Have not tried it yet. But sound like there is a problem with it like i kind of expected. Have you tried this in 1080p mode and not only 4k mode? Remember that the HDMI output is not active while recording 4k video. If it still does not work in 1080p mode it could be two problems. If the problem is that it needs a "handshake" or something from a video monitor to activate the HDMI/sound there is not a lot you can do about it at the moment unless you are good at modding stuff. The other problem could be that the signal from the 3.5mm output is so low level (mic level) that you can not use it with a normal headset. If this is the problem then adding a small headphone amplifier might be a solution (which will also make you able to adjust the volume of you headphones). I have also seen smaller versions of the same HDMI adapter that goes directly from micro HDMI to VGA/3.5mm audio. One of these glued together with a small headphone amplifier and a hot shoe adapter should not be very big at all. I hope someone with the knowhow sees the opportunity to mod these two components together in a nice little box with a hot shoe mount and sell it as a headphone adapter for any camera with HDMI output.
Or even better. If Sony itself would make this. They could make this supersmall by just using the electronics/power from the active shoe mount adapter to give people an (overpriced) headphone adapter for the a6300 and a lot of the other ones that lack this. I would gladly pay 100$ for this item that would cost Sony 2$ to produce. Or they could give people something unique and revolutionary. Headphones with wireless audio monitoring for all their cameras ranging from the f7, via the a7 to the a6300. I dont know if it possible since they dont have bluetooth, but i guess it is possible to do this via wifi signals from the camera since you can monitpr video via wifi. If audio is in the spesifications for what apps can control someone could even do thus via an app on the camera. Or on your mobile phone.
(have not checked if the remote app gives you audio but guess not).
This thing might be the solution for many people. The MuMyk SmartLynk.
I bought one of these while it was on sale here locally (half price). Sadly I didnt know it was the "old" version (non plus version). I thought there was only one version of it but I guess there are two. My "old" version does not give mic power from the 3.5mm outputs so you cant use it with lavs/shotguns like the Rode videomicro etc that needs this. But from the specs it looks like this is included in the new version.
The thing has a battery powered headphone amplifier with seperate output (adjustable volume). Nice!!. And a seperate stereo output for the camera. The thing does however NOT work as an amplifier for the inputs. It is only able to adjust the volume that you put in. But with a "hot" level input like a wireless receiver or a videomic pro it works fine.
But it has its problems Gadgets like this make me wonder if the people who do the design have any experience around what people would need. You can do a lot of stuff with it (disable autogain bu sending a loud tone on the left channel etc). but the one thing it wount do is the most simple and obvious......send one input to the left channel of the output and the other to the right. This only works as a mixer. It mixes the two channels to one stereo signal. Not a big deal for some people but it makes you unable to record two sources at the same time (one with dialogue and one with ambiense) which is what any "professional" would like to do. Dont be misled like I was to think it could. It has a "mix/split selector, but the split only works to send signals to another output for a phone app or something.
If you only need one source at a time you could however just turn down the volume of the other, but this is a lot of uneccesary work. And the volume controls are kind of fiddly and not very easy to adjust.
On the minus side the build quality is just OK (everything is made in plastic). On the plus side this make the thing not too heavy. It also has a cold shoe mount on top to put a shotgun there or any other source. But there is not any place to put a second audio source. So you will have to find another way to mount that (cage, brackets etc).
A (much better) alternative for many is this:
I have used mine for many cameras (gh3, gh4, sony a7s, sony a7ii) and never had a problem. It is pure genious. Really it is just kind of an advanced audio de-splitter but it will let you input two 3.5mm sources and choose with a switch if you want them to go left/right or mix them to stereo. The build quality is fantastic, volume knobs are easy to reach and adjust and with no noise when adjusting them. And the big bonus is that it has three (!!!) cold shoe mounts on it for a shotgun + 1-2 wireless receivers or a light. This works great for cameras with a headphone output like the a7s. But sadly the a6300 does not have this. If you have wireless receiver with headphone output you can use this to monitor that and let the thing put the signal on the left channel along with the shotgun on the right channel. As long as you output a strong enough signal from the sources (and have a good in camera pre-amp like the a6300) I guess you would be able to split the output of this thing. But since the output is a mic level signal you would have to use a headphone amplifier for the signal to your headphones to make it loud enough to hear. Am looking at solutions around this since the mcc2 is so good for everything else.
Hope some of this was helpful for someone trying to work out a solution for this problem. Would also love to hear about other solutions people could have stumbled upon.