Are there any caveats in my SQL migration plan?
Additional considerations for:  


Backup Databases  


WITH COPY_ONLY in order to retain the backup sequence of any third-party tool or backup maintenance plan currently running on your old SQL Server.  

Restore Databases  


You might have to RESTORE DATABASE ... WITH NO_RECOVERY in order to be able to apply further transaction log backups to your new database.  
Or after restoring the database backup run the RESTORE LOG ... WITH NO_RECOVERY on the new SQL Server so that further transaction log backups can be applied.

Single User Mode


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Final Transaction Log Backup


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Restore Transaction Log Backup


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Turn Off Old Instance


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And possible the most important point:

Test Procedure


Test the procedure in your Development Environment