I’m trying to find a solution to exactly the same problem. It seems to me that this is one of those mysterious issues nobody really seems to know anything about; I’ve googled around for about a week without finding a definitive answer to even whether or not you actually can do QoS with a Linux bridge. There are references to such setups here and there, but the examples I’ve tried really don’t work, there’s lots of outdated information out there etc.
I’ll let you know if I learn anything new about this issue. I’d appreciate it a lot if you could do the same in case you come across a solution.