Try to get some live food other than red wigglers. Canadian nightcrawlers are the best. You can offer crickets or waxworms from tweezers. The problem with the red wigglers is that they have a funky smell (and presumably taste), and they are often spat out.
I don't think you need to start over with cycling. If you remove all poo and uneaten food promptly, and keep with with large water changes, and make sure the ammonia stays near zero, the cycling will take care of itself in due time.
Axolotls shouldn't be fed crickets or waxworms. Crickets contain chitin, which is hard for them to digest, and waxworms are too fatty. Ideally, an axolotl should be fed a varied diet of earthworms and pellets.
Red wrigglers can be prepared by soaking, blanching, or freezing (and then thawing) prior to being offered to help get some of the bitter slime off.
Most of the time, gill deterioration (stalks and filaments) is caused by poor water quality. If the tank was cycled, it sounds to me like the cycle must of crashed (as indicated by 0ppm nitrates-- a cycled tank should have readings for nitrate).
The photo looks like the axolotl has some sort of fungus on its face, though I could be wrong.
For now, it's best to tub the axolotl and perform 100% daily water changes. The axolotl shouldn't be returned to the tank until it's completely cycled (when the tank can process 2ppm ammonia into 0ppm ammonia and 0ppm nitrate within 24hr). If the axolotl does in fact have fungus, tea baths can be performed in conjunction to tubbing.