Success!
Hello, gang! I want to thank you all for your help I was truly at wits end. I'm posting to report complete, 100%, unqualified success with the suggestion of Hansr, an app called SteerMouse. Not sure how I didn't stumble on it in my hours of googling, but it's absolutely spot-on. (It even has the thing where it'll automagically move your mouse to the button in a dialogue box nice.)
Even better, in trying to set it up, we stumbled on an even more awesome win (the following long paragraph is detailed and geeky; feel free to skip):
So how it works is the geek at the wheelchair shop plugs my Omni (computer brains) into his PC (they don't let end users do this, which is crap, but I understand; you can hack all the speed & acceleration settings, possibly flipping the chair). For the mouse module, we have four triggers (nudge up, down, left, & right), and four possible actions (left click, right click, scroll up, scroll down). You can assign those however you want, as well as set the nudge time, etc. So we started with: left nudge = right click, right nudge = left click. (Right nudge is slightly less difficult for my physically, so the most common action should be on it.) Right nudge (regular click) worked great, left nudge: nada. We tried making up nudge & down nudge right clicks also. Also, nada. So then we were thinking, ok, maybe there's something about the signal it sends for "right click" that Macs can't read. Hm. So we swapped it, and found that right click worked fine when assigned to right nudge. Other 3 nudges wouldn't do left clicks. So it's an issue with the nudges. We give up and call Permobil tech support. The guy had us do some troubleshooting, none of which helped. He finally suggested we recalibrate the joystick as a hail mary. We go through the recalibration process, which I'd never done on this new chair and found to be a total PITA. And then... ta-da! All mouse nudges magically work! Turns out the joystick calibration was, for some reason, basically phase-shifted to the right, so it was sending stronger voltage signals when it went to the right than any other direction, and the Omni couldn't effectively read it all. This also affected actually driving the chair; I'd found it difficult & always pulling to the right, but thought it was just a combo of my new posture & a new chair, and that I'd eventually have to adapt.
Which means that, in helping me drag-and-drop, MR'ers have helped me literally drive the wheelchair easier and better! The difference was immediate and huge; already I feel like I don't have to think about driving, or using the mouse, which is awesome. This process of getting this new chair has been long & difficult, but you guys helped create a serious bright spot. Thank you, and happy holidays!