Controversial thought: If I'm Elgin, I offer the Catholic 7 plus Xavier (and Dayton/St Louis if you want) a spot in the MVC.
The result: a 20 team MVC. 2 divisions of 10, so you can still play with your old mates reasonably often. You kill the BEast and the A-10 and become the prominent non-football league in the country.
The Catholic 7 will have a home to go to instead of trying to build one from scratch. You latch onto a very stable league. It's better than the A-10 because the MVC deadweight is much better than the A-10 deadweight (Fordham, LaSalle, et al). You can negotiate a TV contract that spans half the country. You have no flight risks outside of the occasional ISU who wants FBS. Can afford to lose a team or two anyways. Secures a place in the top tier of the NCAA.
You have to commit to a big change, and you do leave out teams like Butler, Richmond, VCU, Detroit, and other good A-10 programs, but it's eat or be eaten.