Sounds like a feedback through the power supply during the interval where the 2A3 is conducting but the 12AT7 is still warming up. Or it might be some other cause I haven't thought of. This is the sort of thing that happens when you change the circuit. (We had a similar issue with the Seductor during development, and modified the circuit to eliminate it.)
It's possible that simply changing the final capacitor back to 100uF might resolve it. Temporarily shorting the 10-henry choke with the discarded 270 ohm resistor would at least test this diagnostic guess. A delayed high-voltage start up might be needed to solve it. Probably there are other solutions that have not yet occurred to me.
If you have an oscilloscope, watching the turn-on transient at the 2A3 grid, 2A3 plate, power supply high-voltage rail, and driver plate might give better diagnostic data. Or if you have a SPICE-type simulation software and are familiar with its use, that might give some insight.