Enjoyed the video. Wish I could do that. Nice test equipment too. I have the grand daddy of your function generator, 3310B, knobs rather than push buttons. BTW, what is your day job and electronics background. I suspect we may have similar backgrounds.
I made some measurements on my revibe this morning for you to compare.
My reference was made at the INT pot high side with Speed set to 5Hz and INT pot max CCW (zero). My amplitude was 16.8Vpp. With INT set to max CW the amplitude dropped to 8.8Vpp. This is normal operation because now there is 2.47M (470K + 1M +1M) resistance in parallel with the 10M INT pot. This changes the voltage divider ratio set up by the 4.7M resistor and 10M pot such as to reduce the signal available at the high side of the pot. Nothing unusual about that.
Next, I checked the frequency/amplitude range with INT set to max CCW. Low freq = 3.09Hz, amplitude = 14.6Vpp. High freq = 10.17Hz, amplitude = 11.2Vpp.
Finally, I checked the frequency/amplitude range with INT set to max CW. Low freq = 3.09Hz, amplitude = 8.16Vpp. High freq = 10.17Hz, amplitude = 5.76Vpp.
As you can see, the LFO amplitude drops off at higher frequencies. This is normal but I changed C27 and C18 to allow higher amplitude at higher frequency. This will increase your max speed. (NOTE... the oscillator will stop oscillating if the amplitude drops too much.) You may want to change these caps also. Refer to the notes on my schematic.
I never had any of those hash spikes on my waveform, regardless of the SPEED and/or INT settings. Clean all the way. I believe your hash spikes and low amplitude are related and hopefully will be an easy fix. Start by replacing the tube. Roll several 12AX7s and keep the one that gives the highest amplitude. If still low amplitude and/or hash spikes, replace the LED. I am using a 5mm red LED. If still no joy, check DC voltages on the tube pins 1,2,3 and 6,7,8. Disable the oscillator with your footswitch so the voltages will be steady. Also measure the B+ node voltage that feeds the oscillator tube.
Good luck and report back. I've attached a scope pic but it just visually states some of what I said above. I think your sine wave looks better than mine. Mine seems a little bent on the negative half cycle. Oh yeah, all I did was scope my revibe this morning. I did not play guitar through it.