Conclusions from today:

1) After we were done playing, I hooked up the pedal-only rig with my friend (the drummer, who I usually discuss this stuff with) with the Behringer HA-400 headphone amp. Everything seemed to be in range, though I never did bother trying it without the headphone amp. Anyway, apparently problem solved.

2) There doesn't really seem to be a pad on the mixer itself. We use two digital snakes to get the inputs up to the board, and it's all bridged connections impedance-wise (we checked). The snake outputs in the sound booth are going to the phone plugs in the mixer, so that takes care of that.

3) There is both a pad and preamp gain (and phantom power) options on the digital snake, accessible from the optional remote. For the guitar channel in question, the pad was not engaged, but there was also no additional gain on that channel. If needed, I think we could use that gain from the snake (which does the preamplification for all channels) to boost the signal.

So yeah, the headphone amp/booster did the trick. I'll keep that in mind for the future. Even something like a Bad Monkey, which seems to have a ridiculous amount of available preamp volume in it, might be a decent workaround if I had the drive on it close to zero.

I think I'll try my ampless setup as option 1 next time and bring my amp just in case. Thanks for all of your help!