[EdHolland]

Well that was an adventure, and a successful one.

I removed the transformer, and took off the screening can:

   

After desoldering the wires (noting all positions) removing the nut at the base released the coils, a top disc of phenolic, the mica disc, and its contacts:

   

I found on line a description of using a pencil eraser to clean the mica. This one had clear tracking between the transformer primary and secondary tuning caps.

   

After cleaning, and managing not to break the mica, it looked like this:

   

Wires reattached, and ready to go back on to the chassis:

   

I crossed my fingers and applied power. AM came up nicely, and stayed that way. No sign of the horrendous crashing noises, even after extended warm-up.  Not so FM! Reception has started to go downhill, and with much the same fluttery interference. Part of this was the band-switch - I found a hidden section lurking inside a screening can near the tuner. Cleaning this improved things a little, but FM was still distorted, flickery and a mess. Using my "other radio" trick to probe along the IF chain, I injected a clean carrier and listened on 10.7 MHz. IF1, 2 and 3 were all clean, but at the discriminator, I got the same noise pattern from the probe radio and the Zenith's speaker. Looking at the schematic, there are caps inside the discriminator can. I'll do the same test and treatment on this part. 

Fun day!