Well, it seems I've successfully cloned the drive. It wasn't easy. I mean, not that the steps involved were difficult, but it failed many times (on different stages in the process) and in the end, I have no clue what finally made it work.
I used Parted Magic to ghost the old drive to the new drive with Ghost 4 Linux (RAW Mode, Click 'n Clone). When it was done and When I started Partition Editor, I got an error that the backup GPT was corrupted but the primary GPT was OK. It then asked me if it was OK to fix it but every time it tried, it would display an empty partition list afterwards. Rebooting the computer was the only way to get Partition Editor to see the partitions again, but then it gave me the same "Backup GPT Table Corrupt" error.
After trying a few times without any luck, I started gdisk which also gave me an error message related to the GPT. I went into the advanced options until I found some GPT repair option. I started that and that got rid of the GPT error. But when I tried to resize the partition in Partition Editor, it wouldn't let me. I could move the partition around in the empty space, but I couldn't resize it.
I then downloaded the latest version of Parted Magic. Now I was able to resize the partition but when I clicked "Apply" I got an I/O error during the "gpt_repair -v" step.
I the decided to start over again. I ghosted the old drive to the new drive again. After that I tried to resize the partition again but got yet another error (can't remember what exactly, but I think it had something to do with the GPT not being at the end of the partition). I let it fix that but then I got yet another error (seriously no idea anymore what that error was) I started gdisk and it told me I needed to mount the partition, then unmount it again. Which I did. After that I was finally successful resizing the partition.
So in short, I have no clue whatsoever what caused all these problem - or what solved it for that matter. But it seems to have finally worked.