We raised two turkeys last year for the first time, white broad-breasteds, pretty much the analog to Cornish X chickens. The literature says six months. We kept them almost six months, fed them generously, and let them free-range during the day. One, the hen, dressed out at 24#; the tom dressed out at 44# and wouldn't fit in the oven!
We housed them in a 10' by 10' pen that we have, with a tarp over part of it for shelter from rain, etc.; but, as I say, they were loose during the days.
Based on our experience I'd say take a close look at them at 4.5-5 mos., and if they look big enough, kill 'em and grill 'em (or put them in the freezer for the holidays).
We cooked ours in one of those plastic bake-in bags and they were plenty moist and tender.