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This is Hammond elementary level information, but you are new to this.
To keep the signal/noise ratio low when driving a tone cabinet via a 40 foot long cable that also supplied AC power, Hammond's original 1935 design involves the preamp in the organ sending a balanced-line signal to the power amplifier that's considerably hotter than what is now standard line-level, so the input to the reverb driver is fairly high.
I can test one of the reverb drive transformers for you, but you are correct that there's nothing particularly unusual about the circuit. That the output of the crystal pickup was intended for a balanced recovery stage may or may not end up being significant.
What you may need to do some experimenting with is what kind of damping oil to use in the tubes. I've read a number of suggestions, and I've tried one type of mineral oil, but wasn't thrilled with the results. I tend to think that a very light oil might yield better results. That's where I'd personally like to know more. I know about these things, but I don't get to work with them directly very often. I've never owned one.
I'm David. 'Dave' is someone else's name.