We've done some analysis of tournament seeding in several recent NCAA seasons and determined that the factors that significantly influence a team's seed are RPI, SOS rank, and top 25 ranking. We actually rank all teams during the top 25 ranking process, so there is no limitation to using that.
So the plan to start with is to weight those 3 factors to determine both who gets into the tournament and where they're seeded.
It's possible there may need to be some other factors considered, but the simpler it is the easier it is to understand why one team gets a bid over another. The new ranking system should fall more in line with RPI anyway, so hopefully there won't be cases of ranked teams with low RPIs being out or seeded low.