This is “Star Trek” we’re talking about, and this is the Internet. I’m 100% sure there are people out there who have already collected those laserdiscs and digitized those audio files.
For instance, here is a thread from a Star Trek BBS discussing. Granted, the conversation was ten years ago, but there are people in it who are still active on the site.
Before you go paying a thousand bucks for some laserdiscs, you should reach out to that guy ssosmcin and see if he is willing to donate his LD audio tracks to a fan preservation project. Or just post a request thread over there and see who responds.
Also note that from what they are saying over there, this still won’t be perfect, because the Japanese discs use the third season opening credits for all the laserdisc releases. So you’ll still need copies of the alternate mixes of the theme song. But that’s still a lot better off.