Some might have different experiences but I do not recommend swedish hospital for natural birthing. Group health has a great group of midwives for hospital births. I do billing for several midwives in the seattle area, they're all wonderful! Rainy city midwifery, eastside midwives, lake washington midwives, puget sound birth center, seattle home maternity services, amanda feldmann, cynthia brown, sally avenson. A few of them are nurses too.
MaryAnn O'Hara is an MD that specializes in breastfeeding medicine and also does some family practice and is great too. Marty Ross is an MD in West Seattle that tends toward the natural side too. Susan Moore is an acupuncturist in ballard that works at gracewinds, they specialize in all things pre and postnatal. Dr. Scott Mindel of Belltown Chiropractic is certified in the webster technique (turning breech babies).
I had a great experience though at providence hospital in everett. My OB at The Everett Clinic was Dr. Laurent (Larry) Nicolov. He was recommended to me by an L&D nurse friend, and I loved him! He's highly respected in his field and was really into letting me do what I wanted, especially when it turned out my baby was breech and I wanted to try all the "kooky" stuff. I ended up having a great c-section experience, he and Dr. Jordan were wonderful!
I'm also adding my approval to other's recommendations of expecting the best midwifery, tracey did just have a baby though a few weeks ago and will be out for some time. I know her husband and do their billing with a friend who has been friends with tracey forever.
Let me know if you need any phone numbers or more info, glad there's people like you that care about positive birthing experiences. Welcome to the beautiful Pacific Northwest!