I bought an old Kenmore sewing machine from the local Salvation Army for $4, largely because I wanted this motor. It says it's an AC motor, but I tested it and it's clearly a DC motor, but with a twist: the motor direction doesn't change when I reverse the input current polarity. I don't know why off the top of my head.
EDIT: I just learned that it is a series-wound universal motor that works with AC and DC and can be controlled with a rheostat.
All that aside, it works, I can control its speed just fine, and it puts out some decent torque. I think I found my rotary speaker motor.