I think you're hearing the TT rumble. Is it only there with the platter spinning during the lead-in by chance? If you lift the arm or turn off the motor I'm betting it goes away.
If so those isolation feet probably aren't going to solve your problem since that would mean it's probably not room noise but inherent to the turntable, e.g. coming from the bearing, sympathetic from the plinth or arm or cart or platter with motor noise, etc. Could try a different mat or a different platter (for example the acrylic one Pro-Ject offers, if yours doesn't have it) or you might need a new belt or pulley wheels. Or a heavier plinth or clamp or the bearing needs oil or be replaced.
The one sure solution to rumble is to only play CDs.
FWIW my TT has some rumble and an experiment setting it in box of sand didn't make it go away so I figured, meh, it is what it is. It would probably drive Steve crazy but for me good enough is good enough. I never had the ears to tell and the tinnitus I have has gotten to be a really annoying hissing screech now, a little rumble just rounds out the sound.
Also when you say "hum" that to my EE head implies electrical interference. So are you positive it's an acoustical sound and not electrical perhaps corrosion on connectors or a bad cable? Low frequency hum can come from mains connections, a power adapter starting to fail, crossing cables (think like a ham, sources of RF). The signal from the cartridge to the pre-amp is extremely small so it doesn't take much. Having a WiFi access point near by or a cheap 120V-5V USB adapter (they are notorious for being EMI noise sources).
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