It's good you're getting the saddle issue addressed first, that's the most important thing. I have a mare who is sensitive and cold backed, and while her saddle fit properly, we'd always have back humping and bucking in the first part of our rides. I bought a BOT back warmer pad, mine was around $75, just to try, as I was pretty skeptical about them at the time. And what a HUGE difference! I don't ride in it, but I bring her in, put the back warmer on while I'm grooming and tacking up, so it's on for about 20 mins before I ride. Her back is more relaxed and tons looser when I get on now, since the pad kind of "warms her up" beforehand. The humping and bucking is now just every once in awhile, instead of every ride. And she stands so much quieter in the cross ties with the pad on too, she was always super fidgety and anxious in the barn before, but she just sort of sighs and relaxes when I put it on. So as long as it seems to make her happy and seems to help, I'll keep using it:)
Maybe see if you can borrow a pad for a couple days before taking the plunge to buy? Of course it may not work on every horse, but I think it would be worth a try!