Since Geosword X mentioned that the promo LaserDisc footage wasn't on a CD, I went and put the first song on the disc as an MP3 here:
http://www.mediafire.com/listen/0gsxsynwnsbwixa/G3_Promo_LD_Music_1.mp3
Enjoy 

I did some research, and apparently there are multiple Game Sound Express discs that contain audio from Galaxian 3. Here are my findings:


1..... Starblade (GSE #6)


This includes music from Starblade and Galaxian 3, but it is the music from the GT-16/GT-28 version, not the more familiar GT-6.

Track List:

From what I get of the two scenarios, I imagine one is GT-16, and one is GT-28. They are completely different, but I wouldn't know, as I haven't seen either one or do I have the ability to read Japanese.
I imagine it says in the book, which is, again, is in Japanese.
The oddest thing is that, on pages 7-10, it has a full piece of sheet music for the Starblade theme:





2........Galaxian 3 Project Dragoon Theater6 (GSE #12)


This disc includes all the audio from the GT-6 version of the game, as well as an arrangement of the Starblade theme, likely done from the sheet music on the last disc.

Track List:


This happens to come with a scenario of the GT-6 version, in English and Japanese. In the English version, everything happens with Success, and the Cannon Seed explodes, but in the Japanese version, there are no successes, and, at the end, the Cannon Seed is fired.




3...............The Attack of Zolgear



This is all the music from Attack of the Zolgear, and like the first two discs, the scenarios from them.

Track List:


This time, the scenarios were reversed, with the Japanese version ending well, and the English one ending badly.

And, that's it. By the way, you can download them here:
http://forums.ffshrine.org/f72/namco-game-sound-express-vol-1-27-a-64904/
(By the way, the downloads were not uploaded by me, it just seemed like it would be good to have downloads for the music.)