Why make it a mystery, WHAT amp are we talking about? That way we can look at the circuit you have to work with and have some idea what parameters to consider.
More importantly, just what are we trying to accomplish? Can;'t discuss solutions without knowing the problem. In what way is the reverb sub-par, and what do you want it to do differently? What does improved mean?
I have seen people complain that their amp reverb was wimpy. Why? Because on the Fenders they have plaayed, if you turn the reverb up only as far as 4 or 5, it is already WAY more reverb than even surf music can use, but on their new amp, you can turn the reverb all the way up to 8 before it gets stupidly verbed. Seems to me the "wimpy" one is more useful.
SO does yours sound tinny or dull or weak? Or it doesn;t ring out?
And whatever the deficit might be, how will you decide it is a drive side problem rather than a recovery side problem?
Tube reverb drives with transformers use the low Z input pans, the 4ABxxxx types. Yours is a 4EB or 4FB type, with high Z input. I am too lazy to look up which. SO you are not looking for transformer drives.
One sample circuit to consider is the sort used by AMpeg in some later models, like in the V series.
You mention that we could always add a low voltage supply for a solid state drive. But you started out saying there was already a solid state drive in there, so I would have to guess the low voltage supply already exists.
Primitive or not, what is wrong with the SS drive already there?