Easiest and cheapest option would be to simply do a sub-domain on your current site. I’ve not done sub-domains using RW but I assume RW works normally with sub-domain setups. (If your site is named “mysite.com” a subdomain would be something like “reconstructions.mysite.com.”) Your host should have a tool for creating a sub-domain. Check your site control panel.
Or, as you say, you could go with a completely new site since they are so cheap now days.
Regardless, as others have said above, just duplicate your site and then in both projects remove the pages that don’t apply essentially breaking the duplicates into two separate sites. Be sure to change all the site setup options in the new one as well as the needed page changes.
Or, you could create a new RW project using a new theme, home page, etc and then just drag the appropriate pages from the current site to the new one.