I know it's hard, but forget about the money. If you're not comfortable with your doc, then going public is probably a good idea. There are too many possible regrets if he ends up pushing you down a path you don't want to take.
Who knows, all sorts of interventions might be necessary, but if you go public then you have the reassurance that they will not do anything if not necessary.
A Doula can be a great support for you, but they can't argue your case with the OB or offer medical advice, kwim? (They can remind you of what you're aiming for - natural birth - and help you to remember positions/movements/etc to help during birth). Your DH can certainly question and stand up for you, but - especially in the throws of labour - it's pretty hard to stand up to an adamant OB. It's much better if you're all on the same page to begin with.

All the best~~

ETA - on birth plans. They're a great tool for thinking about what preferences you might have and figurign out what you'd prefer under different situations, but they can mean sqat to OBs if they don't agree with your preferences.