I've got a solution for a situation that is temptingly similar, but unfortunately probably not helpful for your specific case since I'm using partitions instead of user accounts. I have a separate partition for work (specifically a second SSD) because my employer insisted I install remote access software, and that's not going on my personal partition. I ran into a problem where my Bluetooth MAC is the same on both partitions (because it's the same device), but only one partition has the pairing keys for my headphones. On the other partition the headphones see the computer as an already-paired device, so refuse to pair again, but can't connect either due to lack of a key.
I fixed the problem by copying the pairing state files from one partition to the other, and now my devices connect seamlessly either way. I think those files are in /var/lib/bluetooth/<BT-Adapter-MAC-address>, but my memory isn't super clear.