I'm not sure a modded jmp (2204/2203 I assume) will get you the amount of gain you are looking for. And, again, the 2204/2203 circuits are not renowned for their "smooth, full, thick" distortion. Yes, you can increase the gain of the circuit somewhat, and "smooth" it out somewhat, but what I think you will need is an amp with 4 gain stages (the 2204/2203's only have 3).
I think an Orange Rockerverb 50 would be a good amp to try, for your requirements. It also has the benefit that it sounds great at both low and high volume.
perhaps the new Bogner Alchemist (which will be avialable imminently) might well be another good amp to try, as I know it would have enough gain, and have read many excellent reviews of it.
What is your budget BTW ?