FE 300mm F2.8 GM OSS with the 2X teleconverter or stick with

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Have you used and compared the FE 300mm F2.8 GM OSS with the 2X teleconverter to the FE 200–600 mm F5.6–6.3 G OSS for birds and other wildlife? 

I'm considering the FE 300mm F2.8 GM OSS (I already have the 2x teleconverter) to replace the FE 200–600 mm F5.6–6.3 G OSS.

I've scoured the web but can't find many helpful direct comparisons. 

Application, Environment and Background Info

I walk 10-20 kilometres every morning on the southwest coast of British Columbia. It's winter, and in my area that means it's dark and dreary with lots or rain. There are all kinds of birds, from Bald Eagles to Swallows, Hummingbirds and plenty of shorebirds, with many passing through on their migratory paths.  I carry an A1 and FE 200–600 mm F5.6–6.3 G OSS and an A7 IV with a FE 24-105mm F4 G OSS or FE 70-200mm F2.8 GM OSS II for closer opportunities and landscapes. 

I'm happy with the FE 200–600 mm F5.6–6.3 G OSS when the light is good, but I'm in the middle of six months of this rainy season, so I'm usually shooting at 600 mm, f/6.3, 1/500 sec for stationary subjects, and 1/2000-1/4000 for things on the move. My ISO is often above 6400. 

I don't use a tripod or monopod. I'm always on the move.

I frequently crop to 200%. 

I rarely do videos.

I don't shoot sports.

The FE 200–600 mm F5.6–6.3 G OSS serves me well for large birds like Bald Eagles when the light is good. 

Although I'm almost always at the long end (600 mm) of the FE 200–600 mm F5.6–6.3 G OSS, I use the zoom when a large bird approaches or for distant landscapes.

I don't mind the weight of carrying two cameras with these lenses.

Things I hope to change or improve

• Greater agility with a lighter, shorter lens
  I struggle to move the lens fast enough to catch swallows and other small birds in flight. I do much better with the FE 70-200mm F2.8 GM OSS II, but I can't fill the frame with that lens.  I can sometimes keep up with those smaller, faster birds, even with the 2x teleconverter, but I still want more reach.
• Exploring with the 300 mm, fast prime lens
  I like the idea of expanding my photography as I look for subjects I can capture at 300mm at f/2.8 (people and pet portraits outside, musical acts on stage). Although I have tended to use zoom lenses (FE PZ 16-35 MM F4 G, FE 24-105mm F4 G OSS, FE 70-200mm F2.8 GM OSS II), I got the FE 50mm F1.2 GM and have enjoyed having to work with the fixed focal length and how that leads me in different directions. I wonder if I would find the same thing with the FE 300mm F2.8 GM OSS.
• Depth of Field and Bokeh
  I'm unsure if the shallow depth of field and bokeh will make a big difference for me. But I may find that these attributes present new opportunities like the FE 50mm F1.2 GM.

Here's what I think will happen.

I'll use the FE 300mm F2.8 GM OSS without the teleconverter on dreary days. I have used the FE 70-200mm F2.8 GM OSS II (sometimes with the 2X teleconverter) for those days.

I'll use the FE 300mm F2.8 GM OSS with the 2X teleconverter when there's better light. 

Expectations of the FE 300mm F2.8 GM OSS with 2X teleconverter 

• The focus accuracy and speed with the 2X teleconverter will match or better the FE 200–600 mm F5.6–6.3 G OSS 
• The image quality will be at least as good as the FE 200–600 mm F5.6–6.3 G OSS 
  • I'm happy with the image quality using the FE 70-200mm F2.8 GM OSS II and 2X teleconverter and can tolerate the slightly slower focus speed. I imagine the results will be similar with the FE 300mm F2.8 GM OSS but at least as good or better than the FE 200–600 mm F5.6–6.3 G OSS 
• It will be easier to track small birds in flight with the FE 300mm F2.8 GM OSS with 2X teleconverter (1675 grams) vs FE 200–600 mm F5.6–6.3 G OSS (2115 grams). The difference is 340 grams (12 oz) and 5.1 cm in length. That should make a difference, right? 

Questions

Have you tried both? What are your experiences? Will you keep the FE 200–600 mm F5.6–6.3 G OSS?

Are my expectations realistic?

Thanks for reading and thinking about this with me.