Alternatively, depending on how you strategically lay out a new conference, I could see something like this:

Pod/annuals
FSU-Miami-Clem-GT: that's a great football grouping and for FSU, these 3 opponents are also who FSU likes playing in basketball.
UNC-NCSU-Duke-UVA: a great basketball grouping, if you are a ACC traditionalist, then this has to make you smile.
VT-Pitt-UL-WVU: this looks right, each combination would give you a solid football game and very fan friendly for travel purposes.
SU-BC-UConn-Temple: if there is a chance to grab the very populous NE market, this gives you the best chance. I like that all 4 schools are competitively close in football and Temple could probably be had on the cheap for the first contract.

Annual football cross overs: VT-UVA, WVU-NCSU, UM-BC, Pitt-SU, Duke-GT, UL-FSU, UNC-Clem, Temple-UConn. Since these 2 are kinda the football black sheep, I think it makes sense that they play 2x in the season and keeps everyone else from having to play them as often.

With 16 football members grouped like this, you can play 7 conferences games with 4 great annual games a piece and rotate the other 3 conference games. This will free up space to make your OOC games as easy or as hard as you want, plus you'd likely have ND in the mix.