I think private hospitals on the Kowloon side like Baptist and Union are cheaper than the ones on the HK Island side so you could look into that.
About going private in a public hospital, there's a lot of conflicting information. Two years ago, when I was considering that route, someone on this forum who delivered at Queen Mary in the private stream paid HK$40,000 for a private room. At that time, I had signed up to pay $60,000 to 80,000 at Baptist for staying in a ward after delivery. So QMH pricate seemed like a good deal to me, though others migth disagree. However, Queen Mary is too far from where I live so I dropped the idea.Since few people take this route, your best bet would be to contact the hospital directly.
Not sure what you mean by the no privacy policy at QMH...