I would absolutely never give normal-sized (large-fowl, but not huge breed) chickens less than 14-16" over the roost, and more like 2' is a whole big lot better.
Not sure why you're trying to get the roost as high as possible, but it seems to me that the determining thing would be where the nestboxes are; but if you mount the nestboxes so the bottom is like 14" above the floor, that is plenty of room for them to walk (hunker down) below 'em so's not to be losing usable floor space, and if the bottom of the nestbox is at 14" then the top is probably at, what, maybe 2 1/2' (or not quite); so you really needn't have your roost any higher than 2 1/2' to 3' at most. Anyhow if your coop is that short, it is probably also smallish in footprint and the higher the roost is, the more horizontal room they need to get up there and back down, and the more likely they'll find conditions cramped and awkward for doing that. So unless you have some sort of unusual design situation going on, I would think that a 2 1/2' roost would be plenty good, and also give them quite adequate headroom.
Good luck, have fun,
Pat