Oh yeah, it certainly sounds like dental issues. It can be mysterious how they can cope with some foods and not others.
I don’t think switching the pellet brand would make much difference, tbh. You could go to a junior feed rather then adult, to help with weight gain, but do run that past the vet. Have you tried making a pellet mush and seeing if he’ll eat that instead? You can also give Critical Care, mixed up like pudding consistency and given in a bowl.
With pet insurance, there are not a lot of companies that cover rabbits or cover pre-existing conditions. Pet Assure does, however, so definitely check them out. There is also Care Credit. http://www.carecredit.com/vetmed/
Edit to add:
I would probably get him checked out for parasites also. Sometimes rabbits have a low grade or sub-clinical infection that will rear it’s head when they are run-down for other reasons. Their immune system is just too taxed to keep it under control.
Sending some {{{vibes}}} over for your Checkers!