I think Matt's idea is very useful, w/one general caveat. You have to know ahead of time all the file possibilities. Non-suffixed files (Readme, LICENSE, etc.), files not supported by default (file.md5, etc.), etc. would leave folder's partially copied, and this is likely to cause more headache then its worth (in my opinion).
Probably the best thing in this case might be to create a folder list (via Export) and then batch copy the folders.