Dealing with a failed disk in a Btrfs RAID array is not as intuitive as it could be.
btrfs device delete missing
does not just delete the disk from the list of devices used by the array, instead it will re-allocate all chunks that existed on that disk. This means that:
The correct command is btrfs replace start
which will background by default (-B to run in the foreground) and has the -r option to avoid reading from the failed disk.
Additionally, Btrfs arrays don't seem to want to mount in their normal mount point while 'degraded' (i.e. a disk is missing), even if you provide the -o degraded option to mount. Making a temporary mount point and starting the delete seems to solve this.