Well, your steps are pretty much all you need to do, the only other thing I’d do is to use the WP Migrate DB plugin(I personally use it and it saves me a lot of time when migrating the Database) – it supports for change of both URL and paths – you can change one or both of them as well. So here’s your list with my suggestion:
- Put a maintenance message on the site
- Install WP Migrate DB plugin on the WordPress site
- Copy the database, using the above plugin from Tools > WP Migrate DB
- Copy all the files (the hidden ones as well, like .htaccess), with permissions
- Check if there are no old absolute paths, and if so, update them(I’m not sure if you mean in files or what, but I assume there shouldn’t be any in the files)
- Check if everything’s working
- Update the DNS records
- Remove the maintenance message
In theory you can also use the Maintenance Mode for the maintenance message – I know it has the scary message that it hasn’t been updated for over 2 years now, but honestly – I use it pretty much for every site I need to add temporary maintenance mode message and it works just great – I would usually add the 503.php file in the theme directory and make the plugin use that.