How do I figure out what is preventing a bind mount from unmounting?

I have a problem with a mountpoint being too busy to unmount. Normally, lsof or fuser would tell me what process is using it, but this is a bind mount, so lsof and fuser show what is using both the original mountpoint, and the bind mountpoint.

Ex:

Mount the filesystems:

$ sudo mkdir /mnt/mount /mnt/bind
$ sudo mount /dev/sdb1 /mnt/mount
$ sudo mount -o bind /mnt/mount /mnt/bind

Start a process that keeps /mnt/mount too busy to unmount

$ sudo dd if=/dev/zero of=/mnt/mount/testfile bs=1 oflag=dsync

Check what fuser says

$ sudo fuser -m /mnt/mount
/mnt/mount:           4022
$ sudo fuser -m /mnt/bind
/mnt/bind:            4022

Check what lsof says

$ sudo lsof +D /mnt/mount
COMMAND  PID USER   FD   TYPE DEVICE SIZE/OFF NODE NAME
dd      4022 root    1w   REG   8,17    28545   12 /mnt/mount/testfile

$ sudo lsof +D /mnt/bind
COMMAND  PID USER   FD   TYPE DEVICE SIZE/OFF NODE NAME
dd      4022 root    1w   REG   8,17    40682   12 /mnt/bind/testfile

Try to unmount both

$ sudo umount -v *
umount: /mnt/bind (/mnt/mount) unmounted
umount: /mnt/mount: target is busy

If you follow the same steps, but tell dd to write the file to /mnt/bind/testfile instead, unmounting /mnt/mount will be successful, but unmounting /mnt/bind will fail.

Clearly it makes a difference which mountpoint the process (dd in this case) is using, but lsof and fuser do not differentiate. Is there something that does?