Playing high (cheater mouthpiece?)

Probably a question that you seasoned trombone players are tired of hearing, but how do you all feel about “cheater mouthpieces”? I’m a freshman starting in Jazz Band second semester with music that pretty consistently plays in the high D, E, F range. While I can play this high on my 6 1/2 and my 5 mouthpieces, it honestly feels like it doesn’t and won’t sound good - at least not for a while. If it means anything, I’ll probably be playing on a beat up Yamaha peashooter but mayyybe buying a jazz horn. If it’s just a matter of ability, what do y’all recommend to get less “squealy” tone in these upper notes? If getting a smaller mouthpiece is worth it, what size and brand do you recommend? Appreciate it!