The 6AT6 is right in the middle of the filament string. The Riders version of the schematic does not show a cap from the volume control body to ground.
Here's a close-up photo of the area. The Tele-tone service info says to not ground the volume control to the same point as the AC line. That's exactly what they've done here. It's no wonder it picks up some hum.
Here's the Tele-Tone schematic. Looks like someone forgot to bring their compass to work.
Finally, here's the Sams for the Tele-Tone showing C53 on the volume control.
That makes me wonder if Sams was working on both the Meck and Tele-Tone service info at the same time.
First I'll try adding a 5,000pF ceramic dsic cap from the pot body to the chassis. If that doesn't help, I'll reroute the power switch chassis connection to another tie point.