If the upper half of Division I wanted to put its foot down and control the lion's share (if not the entirety) of the NCAA Tournament, who makes the cut? What changes would result?

The big catch is that there are 351 schools in Division I, so the "BCS" would need at least 176 schools to maintain the majority. We start withe the Power 5:

ACC (15)
Big 10 (14)
Big 12 (10)
SEC (14)
Pac 12 (12)

for a total of 65 members. We then add a few close relatives and obvious choices from the non-P5 realm:

American (11)
Atlantic 10 (14)
Big East (10)
Missouri Valley (10)
Mountain West (11)
West Coast (10)

Which brings the total to 131, with 4-5 more conferences needed to reach 176. Who are the last ones in the club? Do some conferences expand to improve their chances? Does one or more brand new conference form to collect as many basketball powers as it can?

45 more?
MAC 12
IVY 8
CUSA 16
HORIZON 9
??
PATRIOT 10

MAC, CUSA, Horizon, Colonial. Just going by RPI. The top half basically already controls the lion's share of the tournament. Only 9 of the 32 conferences had more than one bid, and 6 of those got more than 5 bids. For all the talk of parity in college basketball, it sure doesn't show up come selection time.

If there was a BCS for basketball, I would expect the top multi-bid conferences would "break away" and have a tournament just for themselves with select invites for non-BCS schools just like football. They wouldn't want to give out free units to conferences that don't make the pie bigger. It is even worse when one of those schools upsets a power conference program that steals more units away. So the BCS would make it so the rich get richer and the poor keep begging on the streets.