After quite a bit of searching and calling various Global Entry enrollment locations, I don't have any specific maximum scheduling timeframe. The center I will most likely be using said that they could accept appointments scheduled for as late as January 2016, but stressed that other centers might be different.

I spoke to a few different agents and they all mentioned that if a slot was not available as far out as needed, the best thing to do would be to schedule an appointment for a slot as far out as possible, then reschedule the slot later.