If I understand what you are trying accomplish (which I may not), I think the issue here is why put a free float on a carbine with BUIS (iron sights). Most people who do free float have 20" target bull barrels, quality glass and no iron sights. If you have a carbine length barrel and don't like the stock handguards, I would get the YHM BUIS sights (which are good) and a new handguard (yhm makes an inexpensive, but high quality, set of carbine handguards), and optionally invest in a 4x red dot optic if you want some accuracy at moderate distances (<200 yards).
Trying to turn a bushmaster m4rgery into a target gun piecemeal is likely to cost about as much as getting a whole new upper specifically for target shooting. Uppers are so easy to replace you could go from one to another in seconds and have an all new gun (carbine and target with the same lower). You may want to think about doing something like that.
John @ remsport could probably put together a quality target upper for about $500-600 (although check with him on the costs).