Well, as you have already found out, the private hospital booking system pretty much sucks and is even worse if you are not in HK. Best advice for getting a spot if you were not able to book when you were 5-6 weeks along is to find a doctor who is what they call "resident" at the hospitals you are looking at and see if they can get you in. Try May Mok at the Womens Clinic in Central. She has a good relationship with Matilda and is (or was last time I looked into it) a bit less busy than some of the other docs.
"Worst" case scenario is you deliver at a public hospital. If you are here on a dependent visa you will be eligible. Just make sure to get your HKID card as soon as you can after arriving in HK and go through the registration process with the hospital in your area (the public hospital you would use is determined by the hospital catchment area where you live). A public hospital delivery won't be luxurious, but you can leave in 2-3 days after the delivery if all goes well. There are lots of posts on here about delivery in the public system. The jist of it is that you will get good "medical" care but there are more restrictions on visiting and birthing options (no elective c sections, etc.) and you will be in a ward room with 6 or more others. If you have had a prior c section, they will in almost all cases perform a c section for the next delivery. I know several people who have delivered at public hospitals and all was fine (and ready to get out of there as soon as they could). Also, if you were to have real complications you would be sent to a public hospital anyway because they have all the ICU equipment. Public hospital delivery is very inexpensive, HK100 per day I think. My friends who have delivered publicly have used the money they saved to hire a night maternity nurse for the first month or so after the birth, which was great help on all accounts. Good luck and you will definitely be able to find more useful help on this site.