Yes, I think this will solve it.

In unix, a uid is just an integer (chown <random_int> file will work). In your case, the container created a file in a volume with a uid. This uid makes no sense on host but it leaks out to host anyway since it's a 'volume'.

I think with the userns map, you can map container uid to a host uid. The files created in the volume will then be visible on the host as the mapped uid.

This is my understanding, I have to play with it :-)