Hello - British Airways working-on-the-aeroplane person here! Let me see if I can clear a few things up for you.
Firstly, there are no flights in BA that are 27 hours long. It's not even possible for a normal passenger aircraft to be airborne that long. And BA don't fly to NZ. The last portion of your journey will be with a different airline.
BA do honestly try to make sure that every person who needs a bulkhead seat gets one, but the bassinet positions are given out on a first come, first served basis. It is unlikely that they will be available for general passengers to reserve, as they know that they are most valuable to passengers with babies. However, just because you have a baby does not mean you will be guaranteed a bassinet position. Luckily you have!
Now, there appear to be 2 things distressing you about your seat. Firstly you have not been given seats together as a family. The chances are that each bassinet position will have been requested by a family with a baby. As all of the bassinet positions are at the bulkhead of the cabin, all the babies will be in the same area (subject to the oxygen masks available at each seating position. Different for different planes, and I don't fly the route you are going on so can't comment further there.) It would be unfair to deny another family with a baby a bassinet position just so that you and your husband can sit next to each other.
Secondly, you are very concerned about your husband being given a seat by your baby and not you. Just swap with him. We move people around all the time on aircraft, it's not a big deal to swap seats within your own party. Really! I wouldn't even bother mentioning this to any BA staff. If you want to politely ask at check-in though if they have 2 seats together for you and your husband, go ahead. There may be 2 seats together somewhere else on the plane, but without a bassinet position. Depends how much you want that bassinet. Be aware that the Singapore and Sydney routes are some of our busiest routes, often departing with every seat full - and loads of babies on them, someone else would probably only be too happy to have your bassinet place if you want to sit next to DH!
BA really do try be as family-friendly as they can be. But an aircraft cabin is a very small environment and there is only so much space. It's unfortunate that you have been given 3 different answers, but it is also possible that if you have rung on 3 separate occasions that there had been changes in the bookings on the flight. Flight bookings are incredibly dynamic, and often change and fluctuate right up to doors closing. Most people book a cheaper none-changable ticket, but there are also thousands of people each day who pay more for a fully flexible ticket so they can change their minds at the last minute.
My advice is to accept that you are flying on a busy route and that you are highly unlikely to be the only family with a baby on it, and ask politely at check-in if there is any chance of 2 seats together beside a bassinet position. If there is, hurray! If not, decide whether you want to sit together more, or want the bassinet more. If you go for the bassinet, then you just take the seat beside it without mentioning it. The cabin crew will not be surprised either if you decide to swap seats part way through the flight so DH can watch the baby for a bit while you rest.
Also, bear in mind that other passengers and cabin crew may like your baby quite a lot! I've had Bryan Adams entertain my daughter on a flight once (didn't know it was him till the end of the flight - I could only see the back of his head and kept a close eye on 'that man who has DD sitting on his lap so she can see out of the window!) Other passengers have provided me with lots of relief from my kids over the years, playing peekaboo with them or chatting away keeping them from wailing when my patience at trying to calm them down has failed.
Any other general flying questions, just ask. I can't answer questions about specific flights though.