You should have a look into project config if you haven't already.
It allows you to sync just the structural changes of your development, staging and live sites, without affecting the content/users.
This way you can still sync your production database to staging, but then you can just sync the structural changes back to production – no freezing necessary.
Without having seen your setup, I'd say this is what you need to do:
Move all files and folders (don't forget the hidden ones) to the correct location
Edit your web/index.php file, to make it look for Craft in the right location (it's looking 2 folders up now, it should only be one folder up.
Change your site's base url, in your config/general.php, .env, or ...