Here is the answer that I provided through official support and the ultimate confirmed solution was to move the installation to the domain root and eliminate /new/ altogether; full explanation:
Thanks for your question. Hopefully I understand your scenario correctly. Have you previously been creating subsites the normal way? What do their paths look like?
I’m not sure if even normally created subsites will work with that set up. It seems like that might cause problems with themes and plugins and upload files, etc. because WP multisite will be expecting to reference everything relative to the location in which it is installed ( /new/ )
The Pro version of the Cloner has built in custom site level and global Search and Replace built right in, but even if you use this to replace /new/ with /sub-site-name/ I think you will still run into other problems with permalinks and other parts of WP.
I’m just guessing though and have not played with your specific type of setup before.
If you can move the index.php up to root why can’t you just install WPMS in the domain root to begin with. I think you will have a lot fewer issues in the future this way.
Another option would be to only update the URL of the home page like you want (without /new/ ) but keep all the WP standard structure and links in place for everything else. Not totally sure how that would pan out though.