I would really like to never have users see their UIDs, but I found this situation where they can.

If a user resets eir password and uses the one-time login link that is included in the email, ey are sent to the path /user/[uid]/edit instead of /user/me/edit.

It would be very helpful to me if I could have global instructions for users as well, explaining that profiles may be edited by visiting /user/me/edit instead of bothering with the explanation of UIDs.

Is there a way to overcome this part of Core? I'm using Global Redirect also, but that doesn't seem to do anything in this case.