Found the solution to this issue, for anyone who has the same problem. I noticed that turning off the sound fixes the problem... I didn't like that solution much, since it's hard to tell when you're getting hit without sound and when you're on non-dashboard mode (and dangit, I like the sound of the torpedos)..
So I went through the install process again, this time reducing the sound card from SBPro to just regular SB/Adlib. Now it runs perfectly. Try this if you're having the same issue; just reduce the sound card setting that you are using. Lord knows why this fixes it, but oh well, I can finally play this game again without issues