New answers tagged migration
Assuming OSX 10.8 or later, you could use a combination of find and tmutil tmutil delete <path> will remote the snapshot at <path> while find /path/to/backups/ -maxdepth 1 will list all of your backup snapshots. The last one ( Latest ) is a link to the latest one. You can be a little creative and use find /path/to/backups -name 2\* -maxdepth ...
Target disk mode is the answer. In my experience, there's a pretty good chance it will work even if the display is dead. If Target disk mode fails, you could easily remove the hard drive and connect it to a SATA dock and transfer that way.
mackup does this: https://github.com/lra/mackup I don't have personal experience with it, but i've heard great things. Bear in mind you should check the list of software currently supported by it before you install.
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