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There's an image of the Vertigo CD-ROM on Archive.org and I was able to mount it and install to the Descent II directory. It has its own soundtrack, but if I try to launch with this disc mounted, it says:
Error: Sorry, the Descent 2 CD must be present to run.

If I mount the supplied Descent II image (DESCENT_II.inst) and run, then the game works and I can select the Vertigo missions from the main menu, but obviously the Vertigo soundtrack doesn't work this way.
This question / problem has been solved by arbruijnimage
It might be needed to swap the cd images while in the game. This is possible using dosbox-x:
https://dosbox-x.com/wiki/Guide%3AManaging-image-files-in-DOSBox%E2%80%90X#_mounting_multiple_cd_or_dvd_images
I guess that would work. I have to wonder though, is that the intended way? I've never seen an expansion pack work that way, where you have to insert the original game disc to start the game and then swap it out for the expansion disc.