Darth Mallwalker said:

If target is true 24fps then it's only one step.
Use your favorite software (iZotope RX Advanced if you can afford it)
and convert the DTS files from 44100 to 48000Hz.

Now if the target will be 23.976 it could be a two-step process.
First 44100 to 48000, then 24 to 23.976
But that's resampling twice, and we'd like to avoid that if possible.
We can avoid it! Here's how.
Use iZotope or whatever to convert from 44100 to 48048Hz. Not a typo, I did say 48048.
Then using (SoundForge, Audacity, Audition, Vegas?) to edit the WAV's properties and force the rate to 48000, without resampling.

It's a bit like using AssumeFPS() in the video realm-- it doesn't change the total frame count.
When you force 48048 to 48000 in the WAV's header you're not changing the total number of samples, but rather slowing them down to NTSC speed.
Slowing down without costing the extra step. Does it make sense?

Absolutely right. That's how I've done mine, or I should say doing. I haven't done a SRC to my synchs yet. ESB is doing it now.

Just for the record, you can do it by going to 44144 and SRC to 48000 but its technically less accurate (with a remainder of .144 instead of .048). That's how I did my early synch of ANH that was available on MySpleen, which I've now surpassed.

I have since synchronised the whole trilogy at the native 24fps, 16-bit, 44100KHz (with volume reduction to make it more friendly with DVD/BD's) and am going down this route to match it to 23.976. In fact I've got ESB going through its SRC right now as I finished colour correcting my video source.

In a couple of hours when its ready to mux I'll give it a test and confirm that it works perfectly this way, which I'm entirely confident it will.