This is just a wild guess but have you tried Adobe Media Encoder? I think you can just import the video and export it in a different codec/frame rate. I'm not sure if you would get any juttering or not though because of the difference in frame rate. That's just a guess though.
Digital projectors will pretty much playback what is sent to them. The pitch change and motion difference between 23.976 and 24 is undetectable as far as audio goes and a frame is a frame.
If it really must be 24, and I'd check the specs carefully for the theater because the standard in the us is 23.976, then you could convert it with QuickTime Pro, Adobe Media Encoder, or any other encoding software.
If your original is highly compressed h.264 or other MPEG stream I would suggest re-rendering the project in AE. There will be a significant quality loss if you recompress an MPEG stream.
To change the project in AE from 23.976 to 24 and maintain frame accurate sync all you have to do is change the comp settings and change the interpretation of the footage from 23.976 to 24. If you are using a separate audio track and the project is more than 10 minutes long you may have other audio issues but under 10 minutes there's not going to be much of an audio sync problem. If the audio is in a video track then there is usually no problem and the pitch change is insignificant. There usually is no need to adjust any of the keyframes.
Yes, some theatres will tell you "24p" when they actually mean "23.976".
Verify the truth beforehand.