Cannot save games after migrating PlayStation 3 save files

This sounds like a file call error based on user data saved in your stored game data. I have two solutions, one easier than the other.

Backup your data to a USB HDD then disconnect it. Do not just backup your save game data but also the GAME data. On the new PS3, remove your Skyrim game data. Restart the game and see if you can now load the save data and save over it. If not,

1. Erase both game and save data.
2. Plug your drive in and let it register.
3. Start up Skyrim and see if you can start a new game and load your data off the drive.

Second solution is kind of crazy. Swap your HDD's from your old PS3 to your new one. Back up the new HDD onto your USB drive then copy the data onto your old drive in your new PS3. Does that make sense?

The second should definitely work; the first, I'm not so sure, but the theory is sound. You have a new drive on a new box, so even if your boot name and account are identical, the game data is registered to your old bootname which has a separate unique id. You're wiping the game data from the old drive and thus the old user id. It'll rebuild your game data and tag it to the new id when you reboot the game.