a nice idea but i need something as compact as possible. any flywheeel worth using would add significantly to the size of everything...Record players use an open loop system. Most just use a DC voltage regulator (LM317) to control the speed of a small DC motor. The motor runs at a relatively high speed. A small pulley on the shaft drives a rubber belt that passes around the turntable. The turntable acts as a flywheel, smoothing out the rotation. The torque does not vary so the speed remains constant.
You can buy the belt and the motor assembly with built-on regulator from Aliexpress. It would be relatively easy to construct a suitable "turntable" flywheel with bushed bearings.
EG530SD-3F DC5-12V 3-Speed 33/45/78 RPM Metal Turntables Motor for Record Player - AliExpress 44
