I hear you, Dosbox can be a memory hog.Have you tried adjusting the cycles and frameskip to something that runs the game better? I found that going to an area where there is music and adjusting them until the sound stops skipping is a good way to gauge where they should be.
As for other options, I had the exact same audio chip on my old desktop, and I found no way to emulate sound in a DOS environment through it. The best I can offer in that realm is suggesting that you purchase a Soundblaster Audigy or whatever the new card is, because those tend to work in DOS well.
Aside from Dosbox as a free alternative, have you tried VDM Sound? It's supposed to emulate DOS sound, or the DOS environment, or some such thing that lets you play old games. I've never gotten it to work, opting for the more user-friendly and powerful Dosbox, but if cycles and frameskip tweaking are not working, that might be a good bet.