For $20 you can probably pick up a new Tourney that will run a 34t. I don't know if your Altus derailleur has an integrated hanger or not. You can buy a separate hanger or, I think, you can get a Tourney with a hanger.

My route would be an older used Deore LX or XT, but that is just my preference and have done so in the past. If you did this you would have to get a separate hanger, if the bike frame doesn't have one.

John