From my personal experiences and those of my peers, I don't think you can trick people into discipline by rewriting the application and then letting them in after you've "fixed everything".
First, you are most assuredly deluding yourself about your own mastery of the problem space. The problems you don't see can kill you just as badly as all the ones you do. Two, the bad patterns will sneak back in the first time you are distracted. Which will be almost immediately, because you just made assurances about when major pieces of functionality will be ready to use.
If the team has enough discipline already, you can start refactoring the code to look more like what you wanted. By the time your rewrite would objectively ship you'll be a long way toward it already (and maybe discover some even cooler features along the way.) Refactoring is the Ship of Theseus scenario. You get a new ship but you still call it by the old name.