Two Different Sites With the Same Content. Horrible Idea?

Answer 1

This is the wrong place to ask the question, but it's a horrible idea.

Maintaining the old site at a similar URL will confuse users and only delay the problem rather than solve it. A demo phase (YouTube, GMail, Google Ads, etc did this with their interfaces) where users are given the choice to switch to a new interface (cookies!) can ease radical transitions, but eventually you'll just want to make a clear cut.

If you fear bad consequences for your page rank, make sure the new site is better and redirect all indexed old links to the appropriate new sites where possible (at least for a transitional period).