I tried to work this out a while back, when we were first working on the Quickie. The main problem is getting enough gain; I can't see it with less than three stages. (Using Quickie stages, you'd need about five of them...) The Quickie circuit could possibly be the third stage, with a volume control in front of it - it would rely on having the RIAA stage(s) physically together with the preamp, since a suitable gain stage would have a high output impedance and couldn't drive cable capacitance comfortably. A secondary problem is that the higher-gain tubes usually don't work that well at 36 volts; then want 50-100 volts.
One upshot is twice as many filament batteries, and possibly more than twice as many high-voltage batteries. At that point, you have to ask "how much battery budget is practical for a product?" One approach there would be an inverter to get high voltage from a single D-cell. We're planning to explore that, but it introduces an internal AC power that kills the purity of DC power.
If there's enough interest within these restrictions, I'll look at it again - I have always thought it would be a cool thing. Some people have DC brushless motors for their turntables ...