You can use index.html andindex.php side-by-side easily. That's not the problem that you are having.
The "problem" is that WordPress does not link to http://www.mydoamin.com/index.php it links to http://www.mydomain.com which brings up the index.html page and not the index.php page. WordPress keeps the link to the home page as the main URL without the index.php or index.html or anything else because it's better and cleaner to link to the same URl all of the time (www.domain.com and http://www.domain.com/index.html can be seen as different pages to SE's in some circumstances).
I haven't seen WordPress work with a homepage link to index.php, but I've really only been using it for about 1 1/2 years, so I can't say before that it did or it didn't. Others here might be able to go back further then that.
As I suggested before, what's wrong with setting the site up on a staging server while you get the development done? Everywhere I've worked for the last 10 years has done that because it makes a lot more sense. You have control over what happens, you have control over the code and the database, your client can't lock you out of the iste if they ever just feel like it, and you keep full control of everything until you are ready to deploy it to your clients server.