If I move teams, the money I had to carryover for my previous team just disappears, correct? 

Because if that's the case and I know this will be my last season with a team, then it makes sense to use all my money with my current team to scout states in FSS during the regular season, right? And would you consider this cheap or do you find it alright as a tactic?

It's your money... spend it all. I usually get hookers for the seniors... they seem to focus better after that.
One time I didn't have any players I thought worthy so I sold my HD carryover on E-Bay.... that was pretty sweet as well.