I would do what others have said, add pulldown to the 24 fps stuff and cut it at 60i. When you export for the web it will be 30fps but the 24 stuff will have the film look. I just had to do this for a broadcast show, we have a mix of 24 and 30 and the only way to make it work was to cut at 30.
You can add the pulldown in compressor. It may take a while to transcode, but it will add the correct cadence if you use frame tools.