In the earlier CCG deregulation scenario, events could have changed to prevent the breakup of the Big East. However, I think that the conference's fate was sealed by the time they lost Notre Dame (and Rutgers and Louisville) -- possibly even earlier, before WV, Pitt, and Syracuse announced their departure, back when the Big East foolishly turned down the ESPN deal. The addition of Tulane has been (falsely) scapegoated as the straw that broke the camel's back; IMO the Big East's back was already broken. Once the Big East was no longer treated as a "power" football conference, there was little reason for the basketball schools to stick around.

However, supposing that the conference could continue to survive in its hybrid form, the lifting of the 12-school minimum for CCGs would have given it a better chance to live on. In that case, the scenario presented by Fighting Muskie in the separate thread he created is probably how it would have gone down. The full membership invite for Tulane and the FB-only membership invite for ECU were indeed announced on the same day, right after Rutgers announced it was leaving and right before Louisville did. If only the ECU FB-only invite had been extended, Louisville still would have left, but there would have been no need to add Tulane or Tulsa or give ECU a full ride. So maybe the Big East as we knew it clings to life for a while longer, adding Butler as Muskie proposed to even out the non-FB schools. I suppose even adding ECU as FB-only wouldn't have been necessary, but they had already invited Navy, so having a 10th football school would have made scheduling easier.

The FBS as of 2018 in this alternate timeline (in parentheses = full members/non-FB members/FB-only members):

Big East (8/8/2)
East: ECU (FB only), Temple, UCF, UConn, USF
West: Cincinnati, Houston, Memphis, Navy (FB only), SMU
Non-FB: Butler, DePaul, Georgetown, Marquette, Providence, Seton Hall, St. John's, Villanova

This leaves Tulane and Tulsa in CUSA along with non-FB ECU. I don't think the conference would have expelled ECU for putting their FB elsewhere. They didn't drop UAB in our timeline when they dropped the sport, after all. Here they add Charlotte, FIU, and North Texas because "marketz."

CUSA (10/1/0)
East: Charlotte, FIU, Marshall, Southern Miss, UAB
West: North Texas, Rice, Tulane, Tulsa, UTEP
Non-FB: ECU

MWC (9/0/1)
Mountain: Air Force, Boise, CSU, New Mexico, Wyoming
West: Fresno, Hawaii (FB only), Nevada, SDSU, UNLV

SBC (10/0/0)
East: FAU, Georgia State, MTSU, Troy, WKU
West: Arkansas State, South Alabama, UALR, ULL, ULM

WAC (8/4/0)
FB: Idaho, La Tech, Montana, NMSU, SJSU, Texas State, Utah State, UTSA
Non-FB: CSU Bakersfield, Denver, Seattle, UTA

The MAC and P5 conferences are the same as in our timeline.

NOTE: Here's the alt-AAC if the Big East basketball schools did split away after the moves above. ECU is offered full membership and non-FB Wichita State is added to balance out FB-only Navy, as in our timeline.

AAC (9/1/1)
East: ECU, Temple, UCF, UConn, USF
West: Cincinnati, Houston, Memphis, Navy (FB only), SMU
Non-FB: Wichita State