Hello.
I will need access to hosting account(s).
What web server are you using apache or nginx? Anyway I can configure both.
It is possible to attach new domain to existing IP.
Then there will be little htaccess file wich will detect is it old or not uri .
If it is old uri script will just make 301 redirect to the same url but for new domain.
I can do it in few hours.
First, it will be tested on local pc and then I can share my screen and show you that all is fine.
As about google analytics, please provide me with link to your site and if possible some explanation of how it is configured. It can be no metter where it is placed.
So maybe nothing must to be done.
Regards,
Ivan