Have you tried the security commandline utility? As far as I know it reads anything you want from the keychain. For example, to grab what password Spotify is storing in my keychain: `security find-generic-password -s Spotify -w`
It's some time ago that I tried exporting, so I don't recall exactly what I did. As far as I know, I tried it with that command line tool but it simply wouldn't export everything.
There's also the issue that if it does export something, you have to accept every exported item individually. If you search the internet, you'll find people who wrote scripts for "automatic accept-clicking."
But as I said, once I looked up what it exported, I noticed that it was far from complete.But maybe there's some command line option buried somewhere that will accomplish what I wanted to do...