Hey there~ As someone who did marching band in high school, I would say that compression shirts would work well. You might get hot though, but if it helps you feel comfortable, it should be fine. Just make sure you stay hydrated and make sure you let your ribs off easy whenever you can. Binding while marching is definitely difficult, especially if you play a wind instrument, I would imagine. I marched bass and it took some time for me to get used to. Then I moved to front ensemble and well, I suppose that made it easy for me to breathe, ah-ha~
Anyways, I totally understand how time-consuming band can be, and yeah, unless you're in drum corps every day for the entire summer, you're not gonna get that ripped corps body. I think for you to get extra exercise in is just all about time management. When you have days off, I would say aim to make those your workout days. It can be a lot to manage at first, but once you get into the routine, it should be no problem.
What kind of exercises do you do for your strength training, by the way?