I don't know much about Baptist but a friend of mine gave birth at St.Teresa's. I don't want to be judgemental over St.Teresa's or their practitioners and I'm sure that many women have nothing but praise for the treatment they received there, but this is my friends's story...
The resident OB was quite impatient throughout her latter half of pregnancy and pushed her to have a c-section, saying things like, 'the baby is too big for a natural birth. Why would you want to put yourself through all that pain?' A few days before her due date the OB advised her to have an induction (coincidently her due date was the first day of Chinese New Year). My friend stood her ground and went into labour naturally two days before CNY. She was using homeopathic pain relief and hypnobirthing. After 9 hours the OB decided labour wasn't progressing enough and gave drugs to speed up the process. The result was that labour shut down and the baby went into stress. The OB got her c-section after all. The baby weighed a very normal 3.4kg. So much for being supersized.
My friend was in a private room at St. Teresa's and was told she could have rooming in. After delivery, her baby was whisked away to the nursery and she didn't see her again for 24 hours. Somewhere along the way they changed their mind about rooming in. Her baby was not sick and did not need special care. They set strict hours for visitation and breastfeeding. They even pushed her to use formula because they said the baby was loosing weight in the first few days. Isn't it normal for babies to loose a little weight in the first few days?
Anyway, despite not getting the birth that she wanted, my friend and her baby are thriving and she did manage to establish exclusive breastfeeding in the end.
If you want to have a similar birthing experience as Canada, I agree with Carang that Matilda is the place to go. I've also heard Adventist is supportive.
My OB is also very supportive of natural birth. She is based in TST and delivers at Baptist and St. Teresa's. I can send you her name and number, if you're interested. I don't think she would have any control over what goes on after delivery though.
Erica