Sorry, a little late, but hope some of this will help...
Don't replace the JFet... there are parts matched to it and changing it would throw out the calibration.
The casing of the Jfet goes to ground, if I'm not mistaken. So touching it would affect the audio. Not unusual for it to do that.
I noticed in the top picture there was the metal grounding tape, but not in the second.... did you remove it? If so, put it back... it's there to help with noise.
Depending on your case, it sounds like there could be a part that is shorting out on the case (most likely on the bottom). Some of those cases had metal paint added to the inside to act as an RF shield, but they are also conductive.
Check the polarity of all the caps you replaced, and their values. They are not all the same value!! Also, check that they aren't shorted out on other components.
Check for loose solder causing shorts. I boxes up a Sustainor I modded into a Rev 20 for 10+ years because I couldn't get it to work. When I decided to try again to fix it, I found a tiny solder ball stuck between 2 parts. I removed it and it started working again (still had other things to fix, but that was the main culprit).
Hope one of these leads you to the problen!
A family of high-end analog DI and effects gear.