I have no experience with this sorry, but I just wanted to point out that the scans aren't entirely accurate (depending on the type of scan done, most can be out by around 500 grams) and neither is basing the entire weight of baby on fundal height. I think you should trust your instincts, your body is perfectly capable of birthing a baby born 4kg or more, if you don't want to be induced or have a c/s then don't let them push you into it.

All the best xx