I went back at it today with a fresh perspective, and looked closely
for where the arcing was happening. It was right around the anode
cap, and some of the sparks were jumping a good 2" past the outer edge
of the cap. I ran my finger across the glass (after turning it off,
of course) and there was a little bit if grime on there. I soaked a
paper towel with isopropyl and wiped the entire back of the tube
clean, stopping just shy of the black spray coating at the sides. The
towel was filthy; a lot of stuff came off the back of that tube.

I let it dry and fired it back up. It sparked just a little bit, and
only for a few seconds, then stopped completely. I turned it on and
off a couple times and it is more or less gone. Too soon to tell if
this is a permanent solution, but I'm keeping my fingers crossed.