Aladdin carried a Dolby Digital 5.1 soundtrack, with split stereo surrounds, on some of its original theatrical prints, and that was released the year prior. (In fact, it was Disney’s first feature animation title to be presented in that format.) If a local listing is advertising showtimes in Dolby Digital for The Nightmare Before Christmas, then Disney most certainly had a number of Dolby SR-D prints produced for the release, and it’s likely the same mix that ended up on the DTS LaserDisc.
Speaking of Aladdin, I hope someone is able to find a genuine 1992 print of that film with the Dolby timecode and rip the audio from that…
I know it’s off-topic but if I recall, ripping Dolby Digital audio might seem to be a tricky task to do, mainly because unlike DTS where it’s easy to rip it because of the audio only coming through CD-ROM discs, conversions in foobar2000 and the fact the processor can do digital outputs, the DD processor only outputs audio through analog outputs, so that means that there could be some complex do-arounds on it by just recording all 6 analog connectors at the same time to an audio recording software, unless there are any reverse engineering and DIY tools to directly copy each bit of DD audio in the print to save it to a direct ac3 file if it uses the same decoding as what the DD on LD and later DVD and BD would do. I do remember a couple times where someone would rip the DD audio, such as on the Russian telecine bootleg of Robots, and on a fanmade 35mm 2K scan of the Spanish trailer to the 3D re-release of The Phantom Menace. If you do have access to the file, you will notice that the DD track, being in PCM format, has many analog artifacts in it, mostly analog noise and maybe inaudible buzzing from the analog connectors.