LP12 Hum

If you have a separate ground wire from the Linn to the phono preamp, try removing it. The Rega arm has a strapped ground in the left channel and a separate ground causes a ground loop.

I don’t see any ground wire from the tonearm.

I'm pretty sure I figured out the problem, but my electrical skills are too lacking to fix it myself.  It was the internal wiring of the tonearm.

@theexaltedarchduke , The ground wire is the shield of the left channel so you would not see a separate one. If the Linn is not grounded to the phono stage ground it. If it is remove the wire. 

It could only have been that if you think about it! Dump the arm, the LP12 deserves better.

It was the internal wiring of the tonearm

I say that, because when I pulled the base plug out of the screw shaft, none of the wires were attached.

Best to meter out the connections from disconnected cartridge pins to RCA plugs. 

I used to own a Naim Supernait 3 and I know that Naim can be a bear with grounding issues.  I had to run a wire from the Supernait's ground to the grounding prong on the plug to make it go away.