Used SAL70300G for budget sports photography?

[EtherGnat]

I shoot 5K/10K races and other track and field stuff (serious amateur/volunteer) and I'm looking for a long zoom lens to pair with my Sony Alpha a77ii.

 

Currently I have the SAL1650, a great lens with amazing autofocus, and the SAL55300 which produces great images... when it gets them, but hunts for focus and misses frequently. When you're continually refocusing on hundreds of runners whizzing by that's a problem. I'd like something with similar autofocus performance to the SAL1650 but with significantly more reach.

 

The SAL70300G can be found for sub $400 used, which is an appealing price point for me (see amateur/volunteer status), but I'm uncertain about autofocus performance. A lot of people say it focuses fast and *should* be good for sports photography, but I haven't seen a lot of examples. 

 

Will it meet my needs? Better options? If needed I could sell a kidney and swing up to $1,000 or a bit more but I'd rather not. But then there's also no point in buying something that won't meet my needs. I need something that will focus quickly and consistently with reasonable image quality.