Okay, I've got a work-around/fix.
It appears that something I've done has pushed Glidos' CD audio handling over the edge. The solution? Ditch it and use SAPUCDEX, as VDMSound does.
Following some instructions I found elsewhere from people who did this, here's the procedure.
Obtain SAPUCDEX, and copy SAPUCDEX.EXE and SAPUCDEX.DLL into the TOMBRAID directory. I got my files from my dgVoodoo/VDMSound installation created by Tomb Raider Chronicles' Advanced Installer.
Make a copy of Glidos.bat under a different name - the Glidos UI is liable to overwrite it otherwise. In your copy, add the line "SAPUCDEX" after the line "DOSDRV".
Turn off Redbook emulation in the Glidos UI. Leave Glidos running, but don't use its "Start game" button - instead run your new .bat file.
That then works for me as well as it does in dgVoodoo, including losing the two-second pre-track silence.
Also, you can add parameters after TOMB.EXE in the new bat file.
On a separate note, I did have an oddity earlier where the MP3 support still seemed to be active despite having turned it off. I renamed my Glidos\audio directory to make sure it was inactive.