Attempted to do a little more troubleshooting tonight. I'm still mystified as to what's going on, but at least now I have a better understanding of the problem.
After a little trial and error, I realized that InputAutoCfg.ini writes to mupen64plus.cfg, so anything I put in the former will overwrite the controller values in the latter. Thinking that perhaps whatever issue I was having was specific to Super Smash Brothers, I loaded up GoldenEye 64 also using Mupen64plus-gles2 emulator, and voila(!) the game seemed to be respecting my dead zone values. I had set them to essentially be maxed out, and sure enough I couldn't move the in-game cursor without moving the left joystick to the far edges of its range. I had similar results when I tried Mario Kart 64. I confirmed that I was seeing motion when a joystick value exceeded my deadzone threshold as displayed by jstest.
So I guess now the question becomes, why is Super Smash Brothers ignoring my dead zone settings, but the other two ROMs aren't? Oddly enough, there were a few times when I loaded up Super Smash Brothers and it DID seem to respect the dead zone settings--I had to move the joystick to an extreme to cycle through menu options--but there was no way I consistently get to exhibit this behavior. Is there a config file or something similar that's overriding whatever settings I'm specifying in the InputAutoCfg.ini and mupen64plus.cfg?