At 16 teams, there's no viable way to put all G5 conference champs in, nor does it make sense to. They're simply not better than the teams they'd be replacing.
Which is why I said just carve the non-power conferences out into a separate division/tournament. Why continue to pretend to be in the same division? Every league of anything on earth these days ends in some culminating chance at a title except for non-power D1 football teams.
At that point, why create a third division with so few schools? Why not just play at the FCS level?
Because its about power. The G5 can keep their own rules and say who belongs in their club much like the P5 does. They can continue with 85 scholarships when FCS has only 65 (not all of FCS as BTC pointed out fully funds).
As part of the split the P5 could give up some of their bowls in the process. G5 could settle their champion in a BCS format if they wanted and keep the bowl tradition.