This is the right way to think about it. My only disagreement is that I'd do the local DB before the local service. A bunch of local versions of the service pointing at the production DB sounds like a time bomb.

And it's definitely worth emphasizing that having no framework, MVC, or templating library is not a real problem. Those things are nice if you're familiar with them, but if the team is familiar with 2003 vintage PHP, you should meet them there. That's still a thing you can write a website in.