Convert "Design and Host" to Web Chat project

Hello! I’ve created a relatively complex flow logic in a “Design and Host” project. I realized afterwards that I should have done it in a “Web Chat” project, since I need the functionality (“integration”) to embed the chate on my website.

Is there a way I can get the web chat integration for my already-created flow logic without manually re-creating the entire project in a fresh web chat project? I don’t see a way to import logic from one project to another, and no way to add the web chat integration option to an already created project. Perhaps this can be done on my account from the VF backend? Or through the “Domains” functionality?

I tried setting the projectID value in the web chat javascript embed code to my “Design and Host” project, but that didn’t work. Any hack like that possible?