I am also a prime shooter, but I did investigate all the angles in looking for a 200 2.8 solution. I used my 135L and EF 200 2.8 Lii quite a bit on my 6D and 60D, and would have loved it if they worked on my first-gen mirrorless bodies.
--EF 200 2.8 Lii with MBIV on A6000 and A7R. Focus was slow to lock in and tracking was non-existent.
--Minolta 200 2.8 HS APO with LA-EA4 on A6000 and A7R. Focus was pretty quick--not native-quick, but quick--but would not track. I disliked the the loss in IQ on both bodies caused by the translucent mirror.
Since most of the reason I would need 200mm was sports, I decided to pony up and get a third body--a used A77. I sold my LA-EA4 for $265 and bought an A77 in 9/10 condition from B&H for $369 to shoot a bowl game from the stands.
I ended up using it for a few months, selling it for what I bought it for, and buying a refurbed A77ii for $650ish. Let's just say I'm not sad about the end result . . .
but I was disappointed initially with the inability to use my a6000 with a 200 2.8 prime for sports shooting purposes. I was put in a position where I had to shoot a Spring training game with just MF with a the a6000/LA-EA3 and the Minolta 200, and I was pretty impressed with the IQ of the combo. But, I wouldn't want to do it all the time.
The price of the 70-200 GM just isn't worth it to me, so until I can justify it I'll likely stick with an A-mount body of some sort. If I had to shoot weddings, I would re-evaluate.
Sony A99ii, RX-100ii, Sonnar T* 135mm f1.8 ZA, Planar T* 50mm F1.4 ZA, 24mm f/2 SSM Distagon T*, Minolta HS 200 2.8 APO, Minolta 2xTC APO, HVL-F43M