I don't think a team from the MAC, SBC, or CUSA will ever play in the access bowl unless one of them has an undefeated champion in a year when Boise, Houston, UCF, USF, and maybe a couple of other teams have one or more losses. A one loss MWC or AAC champion might still get in over our undefeated champ, but at least we'd have a shot.
I also don't think that being a recent FCS call up would affect a team one way or the other.