I can answer some of your questions, since I am also from Florida and had my birth with Dr. paer here in Costa Rica.
Regarding Florida, what part do you live in? Even if a hospital is not your first choice, I know there are hospitals that you can do a water birth in. With Dr. paer, it is also a hospital birth. In South Florida, I think Coral Springs Medical Center, and Boca Raton Community Hospital. I am sure there are more, but those are ones I thought about. I would definitely ask around. I also had found a midwife in South Florida who works with an OB if any additional support is needed. She also does water birth in a hospital. Here is her contact information: Judith Kaplan, CNM ARNP
Total Midwifery Care
Home Birth, Water Birth, Private Hospital Birth (Boca Raton Regional Hosp)
Integrative Holistic Women's Health, Hormone Balancing, Gynecology
Kabbalah of Birth Workshops
Childbirth Education Classes
4722 Nw 2nd ave. Suite C108
Boca Raton, Fl 33431
If you do decide on Costa Rica:
The price you were quoted was exactly what I paid. You pay the doctors fees directly to him, then the hospital fees to the hospital. I had my baby at CIMA, which was just like a USA hospital. You may actually pay a bit less depending on how things go. I ended up with some anesthesia and it still was a bit less even after paying the hospital. You will also pay for a few regular appointments at about $100 each.
With citizenship, we first took care of our son's Costa Rican passport. It wasn't too bad. The thing is it takes some time to get it. You won't be able to take the baby out of the country until you have it. All in all, it took about a month and a half. And not back to the USA at all until you take care of all the USA paperwork. You will also need to submit paperwork for a "Permiso de Salida" so you can take the baby out of Costa Rica.
After we had his Costa Rican birth certificate we applied for his USA passport and Consular Report of Birth Abroad. We are both USA citizens, I think if one of you is not yet a citizen you may need some additional documents. We had to provide a lot of documents, which we had brought from the USA. Passports, marriage certificate, proof of time in the USA, letter from the doctor etc. there is a list on the embassy website. You also go to a short interview to submit the papers. Once the papers are submitted, it takes about 2 weeks to get the passport and documents. You can not even apply until you have the original Costa Rican birth certificate, so get that first. The passport cost about $200.
The main thing you probably want to look at is timing. We were trying to leave the country quickly after our son was born and we barely made it at a month and a half after he was born (to Nicaragua) It takes some time. I imagine you are familiar with some of the bureaucratic mumbo jumbo you have to go through in Costa Rica. It always takes a while. If you are planning to live here having a child does give you easy access to residency, but it sounds like you don't need that since you are married to a Tico?
Let me know if you have any other questions!