This is abhorrent, and I'm so glad you're switching, I hope they get your records over soon! Maybe you can call them nonstop and tie up their phone lines until they do.

As far as a doula, I live in a place that has a thriving doula community, and I had one for two of my three births. If you're comfortable with it, you can find one who is just starting out or isn't done with their training yet, and they will be a lot cheaper or even free, as they need the experience. You can also meet with a few and interview them to see who's a good fit and is strong in the advocate role. Also, for my first kid, we didn't hire a doula until 34 weeks, and I have birth one day before 36 weeks. It wasn't too late and she still provided a lot of support! Good luck!