The quick, safe, and easy (compared to making a full backup) approach is
- to set up device mapper manually for the block device to be checked
- create an rw snapshot of the device (with CoW to RAM or an USB stick)
- run
btrfs check --repairon the snapshot
If that works (i.e. the fsck does not rip your (virtual) btrfs volume to pieces) then you can safely repeat the command on the real device.
If this is something you want to try then I can help with the necessary commands.