It was a pain to pull the set apart again, but I think I found the problem.
When the picture goes out, it collapses to a vertical line then quickly fades away. So I figure it must be an issue with the horizontal circuit.
Sure enough. A scope confirms that although the hor. oscillator is running just fine, there's no signal on the 12DQ6 HOT grid.
After a little poling around, I discovered that putting slight pressure on the K5 hor, network in just the right spot restores the raster. I figure there's a cracked PCB trace or bad solder joint under that network.
I wedged a bit of foam against the network and the sets has been running fine for a bout 30 minutes now. Next, I'll pull the board out and fix it properly.