I may be a dumbass.
OK, so I think I have a way around it, and just for future generations, here's what I did:
Step one: Record and trim audio sample. (In my case, some MIDI-driven pads from my Streichfett.)
Step two: create audio track.
Step three: create clip in audio track, load up the sample and place it where needed.
Step four: whack open the mixer view, and in the I/O section set the outputs of that audio track to outputs 3/4. This part prevents the audio from hitting the main outs.
Step five: set the output to a submix. Submix one, in my case, because I hadn't used any of my submixes on this track yet, but obviously it depends upon your circumstances.
Step six: in the effects part of the submixes in the mixer view, set up the effects that you want. In particular, make sure to set the wet/dry mix appropriately for your needs. In my case, this is all wet, all the time.
Now I have a pure-reverb (OK, I added some delay and EQ) result on my background pads.
I hope that this helps other people down the line. Of course, it does mean that I'm using outputs 3 and 4 for something that I don't really want in the audio, but maybe there's an additional subtlety that I still need to unearth.
Sex spreads disease, drugs poison the brain, but rock is still safe.