Thank you very much for the details Stefano. You've clearly done your research!! It makes much more sense to me now and do believe Ulrich's circuit is a good starting place. I also appreciate that you are going the many extra kilometers to eliminate the noise (flame silent) and adjust the frequencies to your needs. A couple of things I don't get about his modulator circuit diagram/designations though.
1. What does TP filter stand for? I get that it is a 1.5MHz filter after the HP filter...basically he has created a band pass between the 2 filters but it seems an odd configuration, almost like a notch filter. Yet the curve shows a clear notch at about 2.6k?? I could be having a brain freeze but don't ever remember one called a TP filter.
2. Why the pull up to 100V feedback to G2 on the EF86. Is that to increase his gain to the ECL82...just seem pretty high? Your coil turns could be why you need more >130V to get it started.
As for the RF side of things a couple come to mind for yours.
First is that Grounding is extremely important as well as shielding. With your transformers on a board and every thing else in the chassis bringing all grounds to "0" is important. A little leakage can be fed into the system and wreak havoc on you grid lines. His shielding also with the perf metal seemed adequate but might consider more of a copper mesh or screen type...more porosity and more wire.
Second is he was very clear that he would build a 3 area system next time for isolation and heat. Again grounding and shielding must be considered strongly but maybe a bit easier to do.
And third the quality of the tube. In your case you have run your tubes to the edge and back several times and may have damaged the cathode/grid connections or warped the plate on yours. Also the filaments may be weakening under the load conditions they've been under. All of that can cause weird things to happen with frequency and capacitance.
The other thing I noticed on the video on FB is it looks like your have many more turns of smaller wire?? Also something about the feed back 1/2 turn and that resistance/capacitance values may need adjusting to temper the feedback to help with your flame control...especially if you are putting 600V into both plates...but may be indicative to damaged tubes?? Also that music/audio on FB was not coming out the plasma right??
It's a fun mystery and sure you will get it. Personally I might roll back to Ulrich's coil/feedback design and try that...if it is still weird check your tubes and grounds/shields. Thanks for the great ride!! ~PJ