Lost Local Items keychain contents, how to restore to new computer

Unfortunately the logic board of my (late 2011) MacBook Pro died. Luckily it was an old unibody model, so I could move my SSD to a similar (albeit older, mid-2009) model and booting up my installation went fine.

The only problem I am facing is that I seem to have lost all items in the Local Items keychain, this includes all my Apple Mail passwords and a lot of passwords I entered in Safari. These were very long passwords I generated to be automatically used when needed, for security.

It seems that the Local Items keychain is not a .keychain file, but a directory with a SQLite database which is used when iCloud Keychain is disabled. Apparently it just created a new directory with an empty Local Items keychain instead of using the existing one. The name of the directory seems to be an unique ID related to the hardware I'm using.

I have already tried to rename my old keychain directory to the UUID of the new one and rebooting, but then it simply renames the user.kb file to user.kb-invalid and starts out with an empty keychain again. I cannot imagine that you always lose all your passwords like this every time your hardware goes defective? I still have the data stored in the login.keychain file, but since I have used Mavericks it apparently does not store all passwords there anymore.

Can anyone tell me how I can migrate the passwords from my old Local Items keychain to the new one?