Savannah State would probably relish an invitation.
However, they have done VERY POORLY (Man, is that an under-statement) since their ill-advised move up to 1-AA.
Davidson, Jacksonville, (and U of San Diego, for that matter) appear to be geographical anomalies in the Pioneer League, but you have to understand that the Pioneer is one of several leagues for Div. I Non-Scholarship Football (is this referred to as 1-AAA ?).
Other 1-AAA FB conferences are the Patriot, Metro-Atlantic, and Northeast. The Metro-Atlantic FB conference is down to 3 of it's own schools (Marist, Iona, St. Peters), and 2 guest schools (Duquesne and LaSalle of the A-10). So there may be some shake-out there. Duquesne had reportedly been sniffing around the Patriot, and making some inquiries.
Anyway, Davidson and Jacksonville are in Div 1 NON-Scholarship FB by choice, and therefore are limited in the conferences in which they can play FB.
Were they to move up to 1-AA, Davidson would probably play ball in their all-sports conference (SoCon) while Jacksonville would have to look outside the A-Sun (which doesn't sponsor FB). The Big South might make sense for Jacksonville, under such a scenario.