Thanks for the link; the article was fun to read!

I managed to compress to ADPCM. (I had to actually do it through my video editing program, but it is super-easy to extract that audio from the generated movie file.) It compressed the audio far more than I could get with my audio software (I cannot fathom how you can get anything intelligible out of 4-bit resolution. Seriously.) and it does sound a lot "better" that way, and tends to match the more "high-end" samples I've heard on the SNES that absolutely had to have come from real audio. It's not working quite as hot for most sounds, but it's certainly a new tool in my belt.
I'm not quite enough of an audio expert to know what you mean by boosting the highs. I tried this filter but it only has an effect on certain sounds.

Okay, so two things I've found:

One, I found somebody who is making a sound synthesizer that will emulate the synthesized sounds of the SNES. He doesn't have any idea when it will be ready, but he did such a good job emulating earlier synthesizers that I think this would be a very useful tool if he gets his project done before I finish with mine.

Two, I have a copy of MegaMan X3 on the PC. (A curious port, it has some snazzier sound and music than the SNES version, plus animated FMV's. I think there's a version on the Saturn that has these as well.) So I sat down and juxtaposed this with the SNES version, trying to get a feel for what my game might be like if I used higher-quality sound than the SNES could use.
I have been able to synthesize a few sounds that match the era, and compress some sampled sounds to match the era, and find a few incredibly generic sounds that I can steal from some SNES games. Using these in conjunction with some sounds that exceed SNES capabilities would help mask those higher-quality sounds. But I think the most important thing to do is to get my music period-correct enough (which looks to be totally do-able) and with that people will be in such a mind-set so as not to notice discrepancies with the sound.

So I think I will be proceeding with the style of re-creating a SNES-era game.

If any of you all have any thoughts on creating the right kind of sounds, whether by downgrading samples or from other methods of synthesizing them, I would love to hear them. I want to get this to fit the period as close as I can.

On a bass guitar forum I'm active on, a lot of people recommend a "bit crusher" distortion pedal. I never really looked into it. This was the standard answer when someone would ask how to make that kind of bass sound.

I don't know if that helps in your situation. Thought I'd offer