Scott - all cables that utilize an architecture where the conductors are not twisted in some manner act just like antennas.
The only difference between your tone arm wires and your speaker cables (for example) is that the signal in the tonearm wire very small and is amplified many times, so even a small amount of noise being introduced into the signal conductor becomes very apparent.
Whereas the noise induced into speaker cables with straight conductors is very small in amplitude compared to the signal from the amp and is therefore much less noticeable.
The same goes for every other cable in your system - including power cables
Conductor architecture and geometry are perhaps the single most important features of all cables when it comes to minimizing noise.
As for the LFD Phono stage, you could try simply touching/attaching a piece of wire that is grounded, to the bare metal of the chassis/case to see if it yields further improvements.
If the slight hum at max volumes you mentioned is still there, I believe it is probably from the internal power supply/transformer.
Investing in a good power cable may be the solution, but if it is not discernable at normal volumes I wouldn't bother.
It all depends on how picky you are - after all, you are an audiophile :-)
Regards...