I experienced a low level hum like you describe for many years, and through many different cable changes it persisted. I tried all kinds of move to improve the situation, and all of my changes in associated gear and cable routing, grounding lifts, etc. never really did much to mitigate it. (Oh, some made it dramatically worse, and were reversed immediately!)
But a cable eventually did improve things, and in a very distinct way. As soon as I installed a used Stealth Hyperphono from the DIN out of the tonearm to the RCA's into my phono stage I have enjoyed hum free LP's ever since. This cable exceeds the stated budget, but it does provide an example that demonstrates that a cable can make the difference. I'm not really sure I can pinpoint just what it is in the Hyperphono's design that accounts for the quiet I hear, but it is doing something right, and hopefully there are more cables out there that can bring this kind of relief for you.