KKH subsidized patient

Hi mummies, I’m currently at week 31 now. My next appointment I’d be at week 33. Would it be too late by then to switch to private? As I’m currently under subsidy. I have no preference on the gynae. Only want to switch cos I’ve heard of “kkh horror stories” whereby expecting mums would be asked to wait for hours during their delivery day before getting a room. And from what I heard, it would mostly happen to subsidized patients. Can someone tell me if this is true?