Sounds to me like your thermostat is junk. Can you first shut down all power, 12 volt and 110 ac. Then remove the screws holding the thermostat to the wall. Next unplug the wiring connector from the thermostat. Now restore all power and see if your blower stops running. If it does, my money is on replacing the thermostat.
Now, who told you the thermostats cost $300? I'm pretty sure you can get one for $200 or less.
Sammie