Carrier high-eff furnace exhaust fan screech

My 1992 Carrier 58SXc060 high-efficiency furnace has developed a screech in the exhaust fan when it turns on. The screech goes away if you grab the motor and lightly move it on its rubber-gasketed mount. This doesn't permanently fix the problem, as the noise comes back on a subsequent startup.
(This may not be relevant, but this problem developed 3 weeks after the Carrier dealer replaced the secondary heat exchanger. This exchanger was replaced under warranty; it is the part that has been the subject of lawsuits and a pending nationwide settlement over corrosion. Mine had not corroded, but its coating was peeling away, so I got a new one).
In talking to the dealer by phone about the new exhaust fan problem, the dealer suggested that the entire motor/fan assembly may need to be replaced for hundreds of dollars in parts/labor.
I do not think the motor itself is failing. Rather, it appears the screech originates within the black plastic fan housing. Before I have a repairman come, I would be grateful for any opinions from people who have dealt with this problem. It has come up on this group before, though the solution was never made clear.
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