Many years ago I had a JMP1 and did the same thing with a Peavey Profex....
You need to check out the section on Midi mapping in the JMP1 manual and midi program change in the GT5 manual.
Everytime you select a patch on the GT5 it should send a midi program change message. When the JMP1 gets this signal the MIDI mapping function allows any of the 128 possible midi program numbers to be assigned to any of the JMP1s patches. So if you just need clean and dirty on the JMP1, say program numbers 1 and 2, you need to map the program numbers from the GT5 to either patch 1 or 2 on the JMP1.
What should happen is if patch 23 on the GT5 needs a clean sound, the MIDI map should send program change 23 to patch 1 for clean - if that makes sense!
It's not as bad as it sounds!