Transfer new website into old URL

I was using the old website builder to maintain a site at http://www.kingstularena.net/ and of course had all kinds of problems trying to make the desktop version look decent on mobile devices. 

After some months of working with the new builder I created a site at https://kingstularena1.homesteadcloud.com/  and every link seems to be working the way we like.

I would like to take down the original site and replace it with the new. I would prefer getting some help with this over trying to it myself; my fear is deleting both sites and having to start all over.

We can't just migrate to the new domain because there are a lot of paper documents out in the public that refer to the original URL and these would be impossible to update.

Can we get some help with this?