There's really never an objective "best" choice, it all depends on what you're attempting to accomplish.
My goal is to achieve the sharpest and most detailed images possible, likely shooting between f7.1 and f9.
Just my personal take, but all three of those lenses are pretty sharp at those apertures:
f/8 is the great equalizer among lenses. :D The 85/1.8 might win by a hair over the other two but probably not enough to make much practical difference.
But you may be aiming for the wrong goal here. Sharpness in portrait photography can be a double-edged sword. Delineating every nose hair, pore, and wrinkle as sharply as possible may not be that flattering (it's why I don't use a macro lens for portraits). You may actually want some thin DoF to help "pop" a subject. And maybe something more in the mid-range of apertures, like f/4 or f/5.6 might still give you enough DoF to cover your subject, but slightly blur a background vs. f/9. And, more importantly, won't be requiring as much power/light output from your strobes. Which can help speed up your recycle times.
You also want to consider working distance and perspective distortion. None of these lenses are likely to be exhibiting much lens distortion, but short lenses, used closer in, tend to exhibit perspective distortion if you try to maintain the same framing, particularly with headshots.
There are reasons some full frame shooters like a 135mm (which, btw, is the center of the 70-200 range), not just an 85mm, for headshots. :) But not everybody wants to deal with the working distance of a longer lens when it comes to connecting with and directing a subject.
Which lens will work the best for you depends on both you and your subject. How close do you need to be to effectively communicate? How are you planning on framing (head, torso, full length?). What apertures and depth of field do you want to use? How much, if any, background blurring do you want? And how much power/spread do you have with your lights and modifiers?
Also, since this is a studio situation, there's no penalty in having all three lenses available to you to choose at will. And you should also give yourself enough time with each lens to know how they'll behave in the space before you ever put a paying client in front of them.