I don't think it's possible. I believe that even more looking at how few teams have won multiple titles. There is something that makes those teams different and I don't believe any conference change can make UConn into PC. We will either stink or we will be UConn.
With Jay Wright gone, there's no real foil for us in the Big East. I think Neptune will fail. Maybe Shaka can do it over time at Marquette, that's the best chance. But Kansas would give us that next level opponent, a real championship contender like we are, that the Big East doesn't have with Wright gone.
I can't answer your final question because I think what makes UConn a "threat to win it all" is that it's UConn. If it gets in, it's a threat. Period. I think 2014 showed that clearly enough. I think you can take Hurley and our entire roster from last year and put them in Seton Hall uniforms and they wouldn't get to the final four. There's a certain mystique around the teams that win in March. We still have it, even after our misadventures.