Yes, an ultrasonic cleaner would help. a lot! Before I bought one, I
soaked the polished piece in sudsy ammonia, periodically brushing
crevices with a soft, old toothbrush. Cheap enough; time-consuming.
To protect your hands, be sure to wear gloves. I like nytril gloves.
Other solutions that will cut the residual polish are out there, and
I’m sure others will share them.
Judy in Kansas, where temps are dropping and the sky is overcast -
precipitation should happen too and will be very, very welcome.