Re: Working with a production company on spec?
I think that the most obvious next step is that you get repped asap. And it sounds like you have enough pitch material to make that happen.
You say that this Prod Co is well known. Then go to imdb and check out a couple of their most recent biggest films. Make note of the writers for each film, a few of the stars, and if the director is a big name, him or her too.
Cross reference those names, beginning with the writers. Maybe the first name is repped by UTA. Email that agent, explain the situation, emphasizing their red-hot interest in you and your script, and tell them the names of the people that you're working with at this company.
I betcha that agent signs you on the spot with all of the advice you need.
If not, move on to the next name.