Is there a way to move a "non-publishing" page to a "publishing page"?

I am currently working on a client's site (SharePoint 2013) and installing Bootstrap (to make SharePoint responsive). In order to make the bootstrap work, I need to be able to change the [Page Layout] within the ribbon.

Unfortunately, this entire site appears to be built with Wiki pages [Site Pages Folder] instead of publishing pages [Pages Folder], which does not allow the users to change the page layout.

So, I need to move these wiki [Site Pages] to publishing [Pages] folder.

I am afraid I'm going to have to recreate all these pages to accomplish this. I've turned on Publishing on the [Site Pages] but it doesn't give me an option to change the page layout.

Any thoughts?!