Experience surviving a change of file ownership on time machine
Solution 1:
I've not done this personally but chown is pretty non-destructive spa recursive chown to make you the owner again is a perfectly valid and safe thing to do. In fact, it's what you are supposed to do when ownership is wrong.
You can always change it back to different ownership later with no loss or risk to file data but given that it is inaccessible right now due to ownership issues, I can't see why you would want to.
Just be very sure you are doing it to the time machine backup only.