I don't know which Solar Winds game you mean, there are two on Mobygames, both from 1993.
Solar Winds: Galaxy requires a 386, Solar Winds: The Escape (Shareware) a 286. A PMMX should be fast enough, though I don't doubt that it feels too slow since you are used to the higher speed.
You definitely found out that it is a speed issue (and of course Quake will run like crap with disabled L1). Maybe it would be enough to run the PMMX at 200 or 166 MHz, though. It should be possible to go as low as 133 MHz with a 2x multiplier, 1.5x is interpreted as 3.5x resulting in 233 MHz. A PMMX is somewhat faster than a plain P1 at the same clock, but not that much faster that I'd expect a PMMX@133 to cause a speed related issue where a P1@200 works fine.
As for the video card I'd probably recommend that you just try to live with the Rage first and if that doesn't work out to use a different card, S3 being an excellent alternative. Since you are already seeing problems it's probably best to go ahead and install the card. Remember to use S3VBE20 and S3SPDUP if you want better performance for some games (S3SPDUP potentially incompatible with some other games).