Okay so when I first started my journey at 275lbs, I was a 44J so I definitely understand what you're saying. As a big-boobed girl, you NEED good support in general which unfortunately means usually you have to pay quite a bit extra. The difference between a bra that gives good support and one that doesn't is the difference between walking tall and a backache, so if surgery is not an option and you're dealing with boob-related back pain, definitely look into making sure you have a quality bra that's giving you good support and that you're wearing the right size. There's a member who used to be active on here but isn't as much anymore who has a site called Braless in Brasil (www.bralessinbrasil.com
) which is an excellent resource for everything big-boobed- from bra-sizing, to brands with pretty supportive bras, to even clothing for a bigger chest.
Regarding your actual question. Your real option is to get a proper sports bra with support. Even now that I'm like a 34E, I don't consider those compression sports bras (S, M, L, XL) to be sports bras, they support nothing! I wear them yes, but over a proper supportive sports bra with underwiring and proper strapping and support. Freya, Panache, Elomi, Goddess etc have some good ones in bigger cup sizes (check Amazon, ebay, google etc). I always wear a compression sports bra OVER my supportive sports bra to further help with the bounce for higher impact workouts.
When I first started working out, I did C25K (a couch to 5km running training program) and Jillian Michaels' 30 Day Shred workout DVD. These 2 were pretty high impact so support was a requirement. As a 44H (pre-knowing about good sports bras/being able to find any in my size), I would wear a compression sports bra over 2 regular underwired bras. My first bra would be a minimizer bra that was slightly too small in cup size, then I'd layer a minimizer bra that was my size over it, then I'd wear a compression sportsbra over that just to be comfortable and reduce the bounce. With bigger boobs, one needs to take extra care, but you can definitely do high impact workouts once you're well supported/"fully strapped in" if you are otherwise fit to do so.
Re: the question of boob-shrinkage... all I can say is sigh! The boobs do not become perkier or firmer in any way with weight loss, they literally deflate in volume. I wanted smaller boobs so badly at my highest weight and now I'd love more volume and fullness. A 34E might not sound that little, but it is when most of it is droopy. In fairness, I didn't have perky boobs to start with (anyone who's naturally a 44J and does is extremely lucky).