A_B: Yes, you'll almost certainly move up to a C- with a NIT appearance.
smorse: BCS are the main power conferences (Big Ten, Big East, ACC, SEC, Big 12 and PAC-10). I would definitely not move to a C prestige in a crummy conference, for several reasons:
1. Your loyalty will take a hit and you'll be stuck there at least four seasons.
2. Your only way into the NT would be winning the CT. If you get upset in a CT game, your season is over and pretty much worthless.
3. It'll take you a good three seasons (at least) to assemble the talent you've already got at GA Southern.
In short, it's a bad idea. You're close, and you may even be a week or so away.
On a semi-related note, I think you are scheduling a little too easy. When you're in a lower-end conference and have a talented team, you need to schedule better in non-con to give yourself a real shot at an at-large NT bid. In reality, that's probably the single biggest reason you haven't been able to move up.
You had a stretch of 6 seasons out of 7 with 18-22 wins and didn't have an rpi good enough for an at-large bid. If you win 20+ games and don't have a NT-caliber rpi, you really have to blame yourself and rethink your scheduling.