All I've done for years is make a copy of the profile folders for backup.
Then on a new system, just replace the contents of the profile folders with the contents of the backups.
This must be done with FF & TB closed, and is essentially what the backup programs do.
Sounds complicated but it's actually quite simple, it's just a matter of replacing the contents of the profile folders on the new system with the contents of the backup profile folders from the old system.
If on the new system you can't find the profile folders in the locations specified, you might have to run FF & TB once for a few seconds in order for them to create a default profile folder.
The articles above talk about making sure folder names are exactly the same etc., that is correct if you want to replace the folder and all it's contents.
I just copy the contents from inside the backup folder and paste those contents inside the new profile folder leaving it's name unchanged.
That way I can name the backup folders whatever I want which makes it a lot easier to keep track of what they are etc...
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