If everything is connected in MOD, then I'd suspect the jumper wiring or the solder joints associated with that path.
Could alternatively be a ALSA config setting, but unlikely unless you were mucking with alsamixer, etc. Have you? If so, I could tell you what to check there. Don't remember off hand.
From your description, it looks like you did try connecting input1 to both outputs in MOD right?
If that doesn't result in signal from output2, then you've narrowed the problem to the output path. I'd verify with an ohm meter that both headers on either end of that short output jumper have continuity. It'll be the lead marked "R" for "right" since that's the second channel.
If that checks, I'd do something similar to check the continuity from the Ring connector of the jack to the "R" pin of the pi-Stomp output header.