I see a few issues. (…and at the expense of some rantings

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The rectified heater supply will only give you approx 7.7 V DC (floating) or +/-3.8V WRT Earth, assuming 0.6V drop per diode (Tony has already flagged this issue). I would suggest a doubler (minimum) and possibly a Tripler for the Positive supply. If you’re really clever you could use a DC-DC isolated converter

. Your power supply MUST have integrity in regards to proper earthing and sufficient voltage/filtering to run the Reverb module. I am assuming a 6G8A type circuit, as this is the best guide you have given us.
Ideally, as Sluckey and others have advised, the optimum insertion point is before the PI (reply #1, #3, #5 and 2deaf #7 and #9, etc) but we have a problem. Obviously the pre PI signal levels are excessive (up to a max of 5Vp-p) entering into the Reverb Module.
So now my difficulty with the Reverb module. It uses TL072 which are fine for line level signals when you want to save current consumption and driving peak indicator LEDs

. You can be quite successful running off a +12V supply modified correctly for 1/2V. Even more successful with Bipolar (say +/-12V) supply and this eradicates earthing issues with Reverb Module, but the module would have to be modified for a Bipolar supply.
This Reverb module uses IC1a as an input buffer, then followed by IC2a (gain as indicated by 2deaf) and processed by BTDR-3 stage which all add up to extra noise. You would need to attenuate the preamp input signal thus lowering your signal to noise ratio, then processing the signal prior to summing by IC1b. Tony has gone to considerable length to as to why you need a substantial power supply rail to maintain your dynamic range (signal from preamp to PI) and I am trying to encourage a good signal to noise ratio.
The TL07x family are not highly regarded for low noise applications and thus while the unit would work on the input to 1st tube, I would not use it for 2 reasons, the extra noise generated due to TL072 and most important you’re TUBE AMPLIFIER becomes a Hybrid! The reason people use TL072’s is for low current consumption and portability generally at the expense of noise and when used with 9V supply or less at expense of dynamic range. You are not limited by low current so is this a good choice or do you modify the power supply capability on the Reverb unit?
You have already indicated issues with built in power supply, thus using battery power and from what you have described, there appears to be some problem with earthing and integration of the Reverb module into the chassis.
My final thoughts: To maintain the integrity of the Tube Amplifier concept, I would encourage you to put your energy into fitting a reliable effects loop. This would maximise your opportunity to do “pedal effects” without being stuck with a possible built-in “dog of a Reverb” and the signal path of the tube amplifier would have the utmost integrity. With all due respects, I’m with Sluckey and Tubenit on this one. And you are halfway there, ie output on the junction of 220k and 22k after the 0.022uF on the main board! Just trying to encourage you

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You really need to “get it on paper”
(Buy the way, I have experience with a few Marshall DFx modules and the joys created

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