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I'm all ears for this one. Please let us know what you find out. There are one zillion gears out there for general use. I'm certain that we can find _something_. The seat just might move at a different speed!
Notice the cracked plastic parts. It is my guess that these plastic parts crack first allowing the clearances to open. The result is particial tooth contact and the nylon gears gradually wear away.
I have found no epoxy that bonds these plastic parts. I have had marginal success in stabilizing these plastic parts by closing up the case with uncured epoxy liberaly appiled to the cracked areas.