There's no way to intermingle two different clusters at the moment. Consider the old cluster completely cut off on its own.
As for moving the two sites, I migrate sites the same way on all kinds of servers = if it's under 1gb size I will use Updraft Plus plugin to grab backups of everything, upload those files to new hosting, update DNS to point at the new hosting, restore the site using updraft and those backup files.
If the site is over 1gb, I use ssh to zip the wp-content folder, dump the DB, use wget on the new server to download the files off the old server, restore the files + db.
If you want to restore the site seamlessly without any downtime using the updraft method, can always use your computers hosts file to be able to work on the new hosting/site without updating its DNS until after the site is fully restored.
If your DNS provider is anycast like Cloudflare, then changes only take a minute to go thru, so it's not like it's a lot of downtime migrating however you want, few minutes never hurt anyone.