I love the 85mm 1.2L It has magical properties. It is slow to focus though. I would wager that if you are shooting portraits and you have a large enough space, you can get better photos with the 70-200L. That is if you want shallow depth of field. I think you can use 200MM and F2.8 and get a shallower depth of field than 85mm at 1.2. Of course it depends on how you frame it, and what distance you want from your subject. The versatility is there with the Zoom. I would say focus speed and sharpness are on the side of the zoom. I think at 1.2 the soft edges add to the look and feel though. Both are heavy. If the 70-200 isn't on your camera due to weight, then I would say look at the 135L as previously mentioned. I love that lens, and if you have the room to shoot it, it has a similar look to the 70-200L, just at 135MM, you can get better bokeh and it is F2.0. Which does help at plays, music performances, etc... Well, just my two cents. Good luck, I wish I was in your predicament.
Tom
www.alicoatephotography.com