Well, I think the first thing you need to do is find out if this is even an option. Then, you need to really think about what kind of birth you want and then decide how/where that's most likely to happen. Your current doctor's feelings and thoughts should not even enter into it. You also shouldn't let fear of change keep you back from the birth you really want (whatever that ends up being).
You sound like you're interested in a natural birth, but scared about being "forced" to have one. Yet, you're also worried about making it to a birth center 45 minutes away on time. If you go too fast to make it to the birth center, you wouldn't have time to get the epi at your current hospital, either! So, wherever you decide to birth, it would probably be a good idea to prepare yourself for a natural birth, even if you decide that you'd prefer getting an epi again.
I don't think you need to take classes to prepare. It's more about mental preparation. Learn about different relaxation techniques and labor positions. Read natural birth stories. MDC is a good source for those. Check out some books on homebirth and read the birth stories (not to convince you to have a homebirth... just to learn how "normal" natural childbirth really is, and see all the various ways women cope).
Provided your insurance covers it, I'd suggest you at least interview the new midwife/OB and take a tour of the other birth center. It's attached to a hospital, right? So, if you really needed an epi, they'd probably be able to transfer you to the hospital fairly easily. Ask your questions, and then go with your gut feeling about which place/caregiver you're most comfortable with.
Melissa , wife to Tom , mom to The Baron , the Bean , Little Bear , and Baby Beaver