you can try Dr Ong Kheng Ho from Douglas Ong Clinic. he has night clinic at Bukit Timah Plaza.
He only attend delivery at Mount Elizabeth and Mount alvernia.
I delivered my baby in Mount alvernia.
Charges wise also ranging from $160 - $200 plus, depending if include medicine and lab test or not.
He has package, last year I signed up is around $2200. I think now is increased already. He will prefer you to have natural birth.