Take two:
As it surprises absolutely nobody, looking up proper adhesives for what you are bonding is better than "YOLO, whatever". It turns out that EPDM rubber (which is something like 99% of what they make shims/etc on nice bike things out of) has two adhesives of choice: a really stupendously expensive specialty product, and well-prepped cyanoacrylate...aka: superglue.
I roughed the surfaces using 80grit paper--stuff they include in patch kits--swiped them with acetone to remove any mold release compound that might still be present, then followed with alcohol, as recommended for bonding EPDM. They warned that you had literal seconds to position your piece, and they weren't joking. Within the space of 2-3 seconds, it was firmly attached to the bonding site. I let it cure for 30 minutes, then installed it and allowed it to finish curing under pressure, monitoring it for creep. It didn't move, and checking it after riding, it was still firmly attached to the site.
Pictures look identical to the first, but it didn't shoot off after riding for 45 minutes.