If it’s been a while since you serviced it, you might be getting enough additional drag combined with a slow sewing speed to make the motor hot. I think I would do a full service (clean out lint, apply oil and grease where needed) on the machine to make sure it’s turning freely before I did anything with the motor.
Lint buildup between the feeddog base and the needle plate can cause gradual loss of performance, but I don’t know if your machine even has feeddogs if it’s being used for FMQ.
I’m not familiar with the Singer 911 machine, do you have a photo?
CD in Oklahoma