As the imaginary conversation goes on, listen to what you are saying and copy down the best parts, just as you hear them. It doesn't matter if the writing sounds chatty or slangy. Once the words are caught in ink, you can clean them up or add to them later. That's what the second, third, fourth drafts are for. Not even professional authors write perfectly on the first try.
Good writing is like cabinetmaking.
It goes through different stages, from rough cutting, through glue and nails, to finer and finer sandings. It also needs time in between for each layer of varnish to dry. Once you've copied down the imaginary talk, your ideas need a chance to settle. Watch a TV show or telephone a friend. When you come back from your break, it's time to fill in the gaps.