K.C.
I delivered my 2nd baby at St. Joe's last October using the Generations Women's Clinic in Shoreview. I had gone to a HeatlhEast midwife meet and greet (which they have every few months at St. Joe's), and really liked them, but went with Generations because there are only 3 (maybe 4 now) midwives in the practice, and I really wanted to get to know all the midwives who might be on call when I went into labor. I made appointments with each midwife, then stuck with my favorite towards the end of my pregnancy. With Health East, you can meet all the midwives at your clinic, but I think since there are several locations, those meet and greets are your only opportunity to meet them all.
Both practices are very open to minimal interventions. I think you're required to have a fetal monitor for 15-20 minutes when you first get to the hospital, but if everything looks good you're done with that. If I remember right, they let you go after a day if everything went fine. Maybe sooner if you really wanted to leave. After the delivery, you go in for a post partum visit at 6 weeks, but I think there's an option to have a hospital nurse visit you at home if you want.
As far as laboring at St. Joe's, I waited until the last minute to get there, and my baby popped out 5 minutes after getting into the room. In fact, a wonderful Health East midwife named Rebecca ended up catching the baby, because my Generations midwife didn't make it in time. Both midwife groups, and the hospital are very supportive of low intervention labors, and I think if you want to be left alone during labor, the midwife and a nurse will check in on you until it's time to deliver. During delivery, I think there would be the midwife, and maybe two labor nurses.
You should take a tour of St. Joe's. It really put my mind to rest, and got me almost excited about a hospital birth, because it seemed so non-hospital like. They also offer water births if you are interested. It's a bummer insurance doesn't cover home births, but if you need to have a hospital birth, I'd say St. Joe's is the way to go.