Thanks for the input, guys!
At first, it looked like RCAman may have hit the nail square on the head-- as he says, there are four resistors right around the 6GH8A horiz osc tube, and one was indeed a tad out of tolerance (R40 measured at 268k instead of 220k). The other 3 were right-on though, and one of those in fact had obviously been replaced at some point in the past.
Replaced R40, switched on the set, and all was OK..! ...for about 10 minutes, and then the HV started flashing on and off again.
BTW, Chad is right that there is no arcing or ozone smell when it cuts out. You can hear the horiz oscillator whine drop and start buzzing, though.
Anyway, since the back was still off, I left the set running and I started tapping poking around with an insulated screwdriver, hoping to joggle the intermittent, but couldn't find it. Several blasts of component cooler spray didn't catch it either. Then I spotted an odd charred-looking spot on C5 (mylar .082uF 600V) in the damper circuit. Tapping the cap near that spot *seemed* to speed up the intermittent, but couldn't be sure. Switched off the set, waited for it to cool down, replaced C5.
I'm not so sure that fixed it though. After switching it on, but still during the "warm up" period, (the CTC-53-and-friends take a loooong time to warm up to the point of producing a picture) I heard the tell-tale horizontal osc 'buzz' for a few seconds, but there wouldn't have been a raster yet anyway. The raster appeared and all worked fine after its normal warm-up time, but I'm still kinda doubtful it's actually fixed-- I guess I'll have to see if it starts cutting out again while it's actually "warmed up". I'm done looking at it for tonight though; I'll come back again to it later...