Took Mickey to the vet's for a tooth checkup, and wonder of wonders, his teeth are just fine and don't need to be ground down right now. The vet said he will probably need to have them done in about 2-3 months from the angle at which they appear to be growing, but right now everything looks good.
I had a feeling he might not need anything done because he's been eating the Oxbow hay cubes I've been giving him as well as some hay, but it was nice to know for sure (even if it did require a half-hour's drive and cost me $28). The vet did say that it looks like this will have to be a life-long thing because of the angle of his teeth, but if we can keep it to twice a year or less, that's not a problem.
When we got home, I took the opportunity while I had Mickey in his carrier to give his cage a thorough cleaning. The tray under his cage was completely clogged up with hay and hay dust, so I've rigged up a small cardboard box to put hay in for him to eat. He has a hay manger, but he seems to like having the hay at ground level as opposed to having to reach up for it. He seemed happy with it, so hopefully all will be good.