Have a chat with your MW first, and see if she would support you in asking for an elective CS. A friend of mine had a traumatic 3 days birth with her first, and tore quite badly. Her MW said if she decided she wanted a C-section for her second, then that is what she would recommend to the obstetrician. She had an appointment later in her pregnancy to discuss the options, OB said it was up to her what she wanted... We're in Chch though, so might have different thinking MW/OB down here.
I've found the majority are quite sympathetic towards traumatic births, and you can usually get what you want through the public system. Might be worth investigating before going straight to private?