General Question About Switching Development Projects

We've been working on and off on a WP Network project for over 4 years now. It has become both a live site and a development hub.

Unfortunately, the development side of it is out of control and we begun to build a clean, fresh version of our project on another domain with the plan being to transfer the new version across to the current live domain when it is ready.

Can someone please point me to the best way to handle this transition?

thanks
Paul