Thanks for the detailed answers. I seem to have missed the fact that the MT7688 has host-only USB. That probably makes the Omega2+ impractical for my project.
I was indeed inspired by these artices for the Pi Zero:
They use the DWC2 driver for device-mode usb on the BCM2835, which allows me to use "arbitrary protocol" USB as described at http://www.linux-usb.org/gadget/. I could even implement my own userspace USB drivers using GadgetFS.
I was hoping to get something similar in a smaller form factor with the Omega2+, which also includes wifi out of the box.
A microcontroller-based solution would be nice as well, I especially like their much faster "boot-up" times, but afaik (I'm not an expert on them) they would require reprogramming for every specific use case, whereas I can just ssh into a linux gadget and reconfigure it on the go as long as it's connected to a power bank.
My current best bet is a Pi Zero with some sort of wireless extension.