Hi BeoAus,
Would you mind sharing with us how this white wheel melted?
All it has on it is a low-tension rubber belt!!!!
At first thought, I'd be looking inside Chinese toys with motors, to see if they have similar parts.
Also, broken CD-ROM drives from computers - most of them have a drive mechanism which uses a similar belt-wheel setup - ask your local computer shop if you can salvage from their junk pile.
I've looked through my junk pile, and that of my son who loves dismantling things, but nothing in the size you want.
Regards
Menahem
Learn from the mistakes of others - you'll not live long enough to make them all yourself!