There are a great deal of variables involved...but, if your problem is that you're not getting the shutter speeds with fast glass and your current camera, then slower glass with a camera with cleaner high ISOs is likely going to leave you right where you are right now. Instead, what you (probably) want is fast glass to go with the 5DIII.
Keep in mind that the 5DIII has Canon's best-ever autofocus system, so the shallow depth of field shouldn't be as much of a problem as you're indicating you're afraid it'll be.
For example, my latest "variables" were a weightlifting competition (Olympic weightlifting movements are explosive and extrememly quick): had my 70-200L at 2.8, my 7D at ISO 3200, underexposed my shots by 1/3 of a stop and still couldn't get the shots due to motion blur, plus hate the noise at 3200 on the 7D. My buddy was using a 1.8 prime and although he was getting the shutter speeds, his focus always slightly off more than it was on.
Sounds like you'll want the 5DIII with fast glass, and that your buddy should probably do an autofocus manual adjustment with his 85.
This page is wonderful for doing the kind of math you're heading towards: