turntable motor speed

No. This is nothing more than a lab-grade highly regulated DC power supply. It's the motor itself that varies in speed, regardless of the accuracy or "purity" of the incoming voltage; you can put a $10K DC supply in front of the "best", most expensive DC motor and it will still drift in its speed stability - not a lot, but enough to be noticeable. Such is the nature of a dynamic load, like a turntable.

While the current-sensing option on the Acopian supply supply will work, my guess is that it will maintain the output voltage within a range of +/- 2 to 5%. Not bad for picking widgets off an assembly line, but insufficient for controlling a turntable's speed. You need something with an accuracy of around +/- 0.1%.

There aren't too many stand-alone DC controllers for turntables. The Origin Live box works OK, but once you pair the controller and the box together you're already looking at $600 or so. Oh, and Mark Kelly made a nice DIY kit controller as well...

So the problem is that it doesnt react fast enough to changes in load? I would be interested to see what actual fluctuations exist in load when turning a fairly heavy platter. I would think inertia alone on a 20lbs platter would smooth out any inconsitencies in load quicker and more thoroughly than any motor controller could. The motor itself wouldnt have enough torque to change a heavy platters speed that fast.

The above should have been 'once you pair the controller and the motor'.

No, the problem (for me) is long-term drift...such as the table running fast or slow up to 1 or 2% over the course of a side (we're talking simple voltage regulation-style control without a feedback loop). All those tiny errors add up. To me, the short-term, second to second errors of a DC motor are fairly benign, though certainly not insignificant when heard in the context of a good AC drive system, given its superiority of torque delivery, accuracy and so-called "PRaT" (and the spectral dividends that result from this approach). At least for me. YMMV and all that...

My experiences with various controller topologies for DC drive would imply a speed accuracy of around +/- 0.1% is achievable under ideal conditions.

Both systems (AC & DC) have inherent weaknesses and strengths; each listener has their own set of biases and expectations as well.