Given a possible BE split and eventual A-10 dissolution here would be an ideal conference and potential 3-4 bid league:
Now 12 would be ideal, but build in 2 extra teams in case of those who get delusional. I'm presuming the BE split will take Georgetown, Villanova, and St. John's (not going to give up that market, especially when SJ is good they generate big attention in NYC). Notre Dame, likewise, would never join this league.
I presume St. Joe's and La Salle are a package deal. St. Bonaventure would be a nice fit for the MAAC (whether they realize it or not). Richmond w/ football would appear to eventually head for the CAA or similar conference.
Duquesne can act as a geographic swing team, as they can fit in either East or West division. This may be necessary due to some myopia on the parts of Marquette, Seton Hall, or Providence. If that's the case with SH and PC, you can potentially lure Drake and Creighton for the West division and move Xavier and Dayton to the East. Additionally, to create 16-team league perhaps Creighton and Drake can be enticed (especially with a looming MVFC) right away.
Given the number of Catholics/Privates in East and Midwest, there are numerous options to fill gaps or provide better fit such as aforementioned St. Bona, Detroit, Loyloa-Chi (a stretch w/ DePaul), Evansville, Bradley, and Siena.
It's important to note that what you are suggesting from the football schools is not entirely a split...it's more like booting 4 members. This leads you back to the rationale for a split: if you are 9 members right now, and looking to improve the football product and stop sharing revenue with non-football schools, why bring in 4 non-football schools to make your existing 16 school conference into a 13 school conference?
I'm on board with Notre Dame joining the football side as the lone non-football school. Especially if Villanova upgrades to be football members #10. The Big East would be in a position at 10 to find (2) more schools like UCF and Houston. If Notre Dame were in, then you bring in UCF for #11 and ECU for football #12, but exclude them from other sports (which Notre Dame would take).
But even with the simple addition of 1 non-football school (Notre Dame), it still leaves you in hybrid mode.
It just seems that if the eventual split ever does come to fruition, that the rationale will be to end the hybrid scenario they are currently in.
As for the other side, as many have said, I think they'll be fine. Providence, St. Johns, Seton Hall, Georgetown, Marquette and Depaul would instantly be able to bring in schools like Xavier, Dayton and St. Louis to get to 9. They'd also have options like Richmond (GTowns top choice)...a non-catholic private school. Can't rule out non-private basketball schools too. Providence lobbied for UMass in 2003 for the basketball side (when a split was discussed).
I don't see a number of the schools you mentioned ever having serious discussions though. Fordham has been a laughing stock...the A10 members wanted them out of the A10...but luckily they've turned things around with some new financing of the program. LaSalle, St. Joes, GW, Duquesne, Valpo..they's guys are on a tier lower than the current Big East non-football schools. There just isn't much attraction by them to the Big east schools.
Also real important to remember that these current Big east schools will have the pride element. It would be next to impossible to envision these schools trading in the likes of Uconn, Syracuse and Pitt for Valpo, LaSalle and Fordham. Not when the remaining Big East schools could just invite the best of the best and have a comfortable 8 team conference.
I mean, even in the dream scenario where GTown, Villanova, Notre Dame and St. Johns are leave, the remaining schools would be better off with just inviting the best options to get to 8:
Providence, Seton Hall, Marquette, Depaul, Xavier, Dayton, St. Louis and for #8, either Richmond, Butler, UMass, Siena, Temple.