The other option is to take the very long view, which would be:
1) cut no one, despite the fact they are awful
2) recruit no one this season, or a D2 1-season transfer to keep a small carryover
3) Go into next season with 6 slots available, start your rebuild there, and start all the frosh recruits so they develop quickly
4) With an empty class, you'd have no recruiting slots in season 73, so you'd get 100% carryover of Big East tournament $$ into season 74...
5) ...when you'd have 6 slots and a nice chunk of change.
You'd be terrible for 2-3 seasons, and you'd be mediocre and playing almost exclusively slowdown for a season or 2 after that. But you could make real leaps forward by season 75. I'm not saying this is "correct" or even that I could stand to do it-- but you do need to consider the long-term impact of slot management when making your cut decisions.