You're overestimating the importance of prestige in DII, it really isn't that important. Sure its something to take into account when determining whether or not to battle someone, but you have to look at the big picture. In DII I took the following factors into account when considering a battle, in order of their importance:
1. Number of open scholarships
2. Distance advantage
3. Conference prestige (for postseason success/bonus recruiting money)
4. School prestige
If I felt like I had an advantage in those categories (in particular the first two), then I would go ahead and battle for the recruit. As a B- prestige, if you have a distance and scholarship advantage, you can absolutely win a battle against an A+ team.
The real importance of prestige in DII is that A+ teams will have immediate access to better recruits right off the bat, while B- teams will have to pull those same players down (if they are even recruitable at all).