OK, so even though DVD Audio Extractor only showed 3 streams available (96khz stereo, 48khz DTS, 48khz DD), I extracted the one called DTS. Uploaded a track in Audacity, and it tells me it's 96/24.
For backwards compatibility purposes, DTS 96/24 basically piggybacks the extra 48kHz of frequency response on top of a standard 48kHz DTS stream - if you have an old "vanilla" DTS decoder it only sees that basic DTS data, but if you're 96/24 DTS capable it adds on the extra resolution on top.
For some reason DVDA Extractor only reports that 48/24 stream even though it actually transcodes the full 96/24 resolution, as you've experienced. I don't know what the reason for this, it could be just an oversight in the coding of the user interface, or possibly they're not actually licensed for DTS 96/24 (I have some recollection that that's why they used to not be able to transcode DTS-HD streams?) so they can't advertise it, but either way, you definitely get the full resolution from DVDA Extractor.