After searching for a while, and finding nothing but posts that said “you can’t do that”, I did a little poking at the files myself.
To copy a Scene to another Show, extract both showname.bz2 files. The trick to it is that there’s some kind of index file. You can’t simply drop a new scene into the Show archive, you have to overwrite one that’s already there. Note the slot number (nn) of the scene you want, and copy the desired scene files, FilterPatchnn.dat & Patchnn.dat from the extracted Show/Patches directory. Change the file names to match an existing redundant scene in the target show. Copy overwrite the redundant scene files in the extracted target show. TAR the Show directory. BZ2 the TAR. I used the Mac app Gui Tar 1.2.4 for that. Load your new show.