"corrects for drag instantly...."
Not possible. Instant velocity change to the correct velocity would be like a perpetual motion machine.
Fast correction = flutter.
Slower correction = wow.
Slow correction = drift.
All affect the music. Correction (servo circuits) are bad for this application. It's why no master tap machines used them, which is directly addressing the OP's stated problem, his DC turntable's speed problems. DC motors need servo circuits, and those are very compromised for this particular use, high end turntables.
Everyone thinks they have great speed stability in their turntables until they hear one that does, then they wonder why the stable one is so clear, so natural, so right.