First need to determine correct terminolgy from the OP. There is a difference between a fan motor for exhuast and a blower motor. For $800 I'm guessing it's the blower motor (added the fact that the exhuast fan motor really shouldn't have an affect on running the AC, but the blower motor would).
I installed my 80% variable speed gas furnace with a heat pump in my attic around 2004. Last year my blower motor went out. One of my few work perks is I buy directly from the manufacturer. As noted, I believe what the OP is refering to is the blower motor. My cost on that variable speed constant airflow ECM motor was
WELL over 50% of the cost of what the OP was quoted (and my luck, it was past the 10 year parts warranty). If he gets it installed for $800, he wouldn't get ripped off IMO. As far as moving parts, need to look at the blower housing assembly as well, which includes the blower wheel).
Customers expectations are that if the unit is making a noise and it's diagnoised at being the blower motor, if the motor is replaced and the furnace is still making the same noise, the contractor should make it right and fix the "real" issue at no charge.
That said, if the gas furnace was installed in 2013 and it was registered, it should have a 10 year parts warranty, which means ANY part would be free, but the OP would still have to pay the labor to change it out. Since it was installed in 2013, not certain why it wouldn't have a 10 year parts warranty?
Carrier came out with on of the first variable speed ECM motors in the 1990's. Cost back then for the motor was about what I paid for mine in 2019 (20 years later). When I first saw the cost of the motor (not what the contractor pays for it) I remember joking to a guy back then that "dang, the cost of this new motor costs only a little less than a complete new gas furnace."
Due to FER regulations, PSC driven gas furnaces are no longer being made (those are the "cheap" permanent split capacitor motors that you could buy all day long for under $120 at supply houses). Every furnace now being produced (including electric mobile home "furnaces") now have at least the much higher priced constant torque ECM motor (AKA the X-13 back in the day LOL).
FER Standards Require Electronically Commutated Motors | 218-1-29 | ACHRNEWS
On a sidenote, we can thank California for the higher priced blower motors. Still more stuff coming down the pipe in the next couple of years due to that wonderful state.