Hum decreases with tonearm position. Huh?

To all of you experts:
Help, please. This is making me crazy.
I've got an annoying hum coming when I use my turntable. Here's the setup:
Rega P3 2000 with Elys cartridge;
Ray Samuels F-117 Nighthawk phono preamp. (This is a battery-operated unit.);
Wyred 4 Sound STP-SE preamp;
W4S mono amps (I forget which models. Not the lowest, but not the highest.);
Celestion SL-700s.
Everything is plugged into a PS Audio Power Plant Premier.
The preamp is connected to the amps with W4S XLR interconnects. The TT to the Ray Samuels is via the dedicated cable on the P3. I've tried various interconnects from the phono pre to the preamp with no difference.
Here's the story: There's a hum, which can be heard with the volume set even fairly low, at even low listening levels. But it is loudest when the tonearm is in its resting position, lessening as I move the arm toward the spindle.
I've tried moving the preamp away from the TT, but that doesn't change anything.
The hum isn't so loud as to interfere with listening to records, but it is loud enough to be very, very annoying when I'm, say, getting ready to spin a favorite platter. Or when I'vm flipping one over.
Any thoughts about what might be causing this? My cartridge is getting a bit long in the tooth -- I've been thinking about an upgrade -- but I don't see how that could be causing this. And I'm not really excited about dropping some real green on a new cart until I've got this hum thing resolved.
Is it odd -- it seems so to me -- that I've got hum with a battery-operated phono preamp?
Thanks so much for any help you might be able to give me with this.
-- Howard