I have also lost a "battle" to a DIII team. It was a backup player that I didn't prioritize until other options had expired, so I only had 280 AP. However, I promised a start and 25 minutes and had a preference advantage. He did not offer a promised start nor minutes, but did offer 20 home visits and 1 campus visit, whereas I had no budget to offer those. He was an A+ DIII, I was C- DI Stanford. Final odds were 66/34 in my favor.
The best solution, in my opinion, would be to drastically increase the gap in preference advantage between divisions. On top of that, improve Sim AI recruiting (since the worlds are not going to fill up) such that they actually recruit with any modicum of intelligence. Caps and even the existing inability for DII and DIII to sign up in RS1 are just patches on a broken system that needs internally fixed and fine tuned.