[skyscraper]

Here's what I have so far. Since it sometimes works with wires touching various points of the oscillator, I'm going to assume the other five circuits are functioning correctly for now.

It occurred to me to play with the value of the cathode resistor, like I mentioned earlier. By raising the resistance closer to where it was originally (10-13k) I can get it to oscillate a few hundred kilocycles lower. But it didn't fix it, I can't receive strong stations at 560 and 620. 840 and 890 are now coming in, so some improvement.

The options I can think of now:

Change 36 cathode resistor to 10k. Seems to help.
The plastic insulator on the coil, or perhaps the clear coat lacquer, is interfering with the field
The cathode capacitor is a cheap 680pF Y5P, maybe replace with a higher quality more stable cap.
Find a NOS 36 tube, most of mine are used but supposedly tested excellent.
The (secondary?) winding under the tickler has a few small spots of green corrosion. Ohms out fine, and there is no continuity between the surface and the windings.

I think I can rule out all the variable capacitors, they seem to work fine. Does anyone have any further suggestions, or where to start?