It's a bit late but get in contact with the gasthof zillertal. They do cheap accommodation for the season. It's a bit out of town but it's on the free bus route between the town and the horberg lift.
Also if you're German is good, try the ads page on the local newspaper site. https://www.heimatstimme.at/de/anzeigen
Other than that, find a cheap bnb and go out for a while and have a look in town.
Seasonaires Accommodation in Mayrhofen is a real problem.