Other physical remote options for a Mac (not an iPhone or iPad)
Eventually, I answered my own question.  For the sake of hopefully helping anyone else who may be wondering the same thing, here's my answer:

I asked: "Is there any other remote that would work with a Mac other than Apple's remote, in order to get more buttons to reassign?"  The answer is yes!  It's possible to use two Apple remotes, assigning different functions for each, and it's possible to use a universal remote with a Mac, assigning any functions you'd like to any buttons you'd like.

I found two options for doing this.

There's a usb receiver called Flirc that learns remote buttons for just about any remote and then assign actions or hotkeys.  And, there's an App called Remote Buddy which allows you to use more than one Apple remote and/or various other remotes.  I can't say how well it works since I opted for Flirc.

Basically, I have two Apple remotes - an old white one and a silver one.  I wanted to use the white one to control my Philips Hue lights via Applescripts I wrote, and I wanted the silver remote to control iTunes and system volume.  Using Flirc (and the free BetterTocuhTool app), this was astonishingly simple to set up.  Once I realized how flexible Flirc is, I also recorded functions for my universal remote.  I've only had Flirc for a few days, but I'm really thrilled with it.