Looks like a plastic box? I don't think there'd be a huge problem with your dads proposed solution as long as the screws go straight up. One problem with it is it's something that'll fix the problem until the next time the box comes out. That might be never if you aren't doing anything that'd need you to open the box again.
I bet you could get a tap one size up and just cut new threads at one size larger too. Nice thing about that is you still have nice machine threads and the original material so you can remove the screws if you need to.