Reed Muse 3C turntable

Any owners in EU?

I've since added a second battery (in series) and that produces 24v.  I then use a linear voltage regulator (with adjustment knob and digital readout) to deliver a steady, consistent, and exact number of volts to the table.  The motors can run on anything between 10.8 to 13.2 and right now I'm delivering 12.9.  The speed fluctuation on this table is vanishingly low according the measurements I see on my "Platter Speed" app.  More importantly, music simply sounds right, in a matter-of-fact kind of way.

Exlibris, Two thoughts on your battery power: (1) Strange and pointless as it may seem, you may hear an improvement if you bypass the battery or batteries at their output with large value capacitance.  Try some huge value 16V electrolytics with the pos terminal connected to the pos node of the battery output and negative connected to ground.  16V electrolytics are small and cheap, relative to their capacitance, so this is a cheap tweak. Yes, batteries already make "pure" DC, but it's not perfectly pure; there is some high frequency noise generated as well, and in addition, the capacitance will reduce the output impedance of the power supply, always a good thing, and (2) always disconnect your charger when listening to music.  The charger itself can inject noise into the power output.

lewm,  Thank you for the tip on the electrolytics; I will try that and report back.  
I always disconnect the charger when listening to music because it injects noise that is clearly audible.

lewm,
The two 12v batteries are connected in series and the 24v output connects to my voltage regulator with a pair of banana plugs.  
Would connecting a single 35v capacitor at the input of the voltage regulator have the same effect as what you suggested above?