I've added the dtshd extension for the next build. And as far as I can tell, it plays them in their full HD glory just fine (even if renamed to .dts). As Roderick points out, you can always check the "Compression" tag to see which profile it identified them as - or a combination of Channel and Bit Depth and Sample Rate, since for example 24-bit is only available in HD, or anything above 48000 Hz (or 8 channel, but thats more likely for movies then something you would want to extract as audio).
If it played as 24-bit as you said in your first post, it would've had to decode the HD part to get 24-bit already. The Audio Path only shows the file type, not the actual codec profile, unfortunately.
It sounds a bit backwards, but if you have DTS-HD MA (ie. lossless), you would get Bit Depth 16 or 24-bit (Integer), while if you play the DTS Core, you would get 32-bit (floating point), which is just how the decoder works.
In Lossless the original 16 or 24-bit integer audio signal is being fully restored, in lossy core mode it decodes to floating point audio, which is always 32-bit. That way you can always check if its decoding core or HD, but i'm pretty confident in our DTS-HD decoder.