While I had asked the hosting company for a sub-directory to assemble this new site, in practical terms the new.sitename.com appears to be acting as a completely new domain name and that is how it appears in the CPanel.
I have a primary domain and a few add-ons (but no sub-domains), and I readily admit to not knowing how all of that works even though I do know how to use cPanel to assign and/or redirect my domains to wherever I want them to land. The bottom line for you here is to simply know where sitename.com is assigned to land so you can put all-new wp-folders and wp-files.php plus your current new.sitename.com wp-config.php file in that location and run it *after* having told that new database the new URL to expect and to use.
Additionally in looking at databases stored under sitename.com and new.sitename.com they are completely different - here I am looking at the list of databases not just the ones being used.
cPanel > MySQL is where I can see all my database names and users, then cPanel > phpMyAdmin is where one of my users with full permissions for all databases can see all databases and their table_prefixes at once...and that is why there should be no need for you to do any database exporting/importing. If you can see a list of databases and both databases are visible there, your wp-config.php file will find its desired destination no matter where it is placed.
It seems to me that in taking the path that I propose I may be doing a bit of overkill potentially, but it should work fine. Is that a reasonable take on this?
I have only one eye that can read, and I have not studied your plan in detail. However, I had not seen anything there about changing the URL in the new database to make it work with wp-folders and wp-files in any place other than the new.sitename.com location, and doing a database export/import will not address that matter.