I don't consider this arrangement to be 'mucked up' at all
What I mean is that a file manager, which Finder is, should be showing you the folders and files exactly as they are. That's what a file manager does.
I wish there were a way to extract all of the files in the AVCHD or 'Private' file
That's generally a bad idea. Like Craig says, you should be keeping the Private folder intact and unaltered. The media will usually work better that way.
If you want a way to see the individual clips outside of PP more easily, talk to Apple and get them to fix Finder so it works correctly.