I haven't yet modded the module… the amplifier is powered by an on-board linear power supply (the rectifier bridge and filter capacitor is seen bottom right of PCB).
I really should remove those capacitors, but figured I'd do a test with the board as-is, since in theory it should work. The turntable I have (a Kenwood P-110) features a pre-amp in it already. Turntables that don't, probably will need to hook up to that JST connector instead.
As can be seen here, a bit of level adjustment and I was seeing the waveform in Audacity. As a bonus, I don't have the tinny audio problem that the now dud turntable gave me (RIAA filtering? What's that?).
So I think a bit of careful SMD part removal, and I should have exactly what I'm after.