It is not necessary to loose the powersupply connector of the
display, the display can be left connected and lifter on th eright
Use Migration assistant and select your time machine backup.
Users already existant on your new mac will have a red This user needs attention.
When you continue you have to choose between the new and old user. There is no option to merge.
It may be a good idea to use a new user when installing your new mac from scratch...