Hey, Sarah,
If you have a very bad back, the 11.5kg Oyster 3 might be too much, It pushes nicely enough, but the handle rattles a bit on bad terrain, and I was carrying it upstairs in my hands, and must say that is not an easy task. With such problems, you need something considerably lighter, I believe, however I feel the larger wheels can be a problem in that case - not many strollers combine those features.
I personally would compromise on the seat here. YOu can go for a non-reversible stroller compatible with a carrycot and a car seat, it will take about 2-4 kg from the overall weight, and that is considerable. I personally would look at the Baby Jogger City Mini GT2, which offers a carrot option as well as Maxi-Cosi/Cybex adapters option.
Apart from that, check the very light Valco Snap Sport, which, with those SPORT inflatable wheels, makes up for a good compromise. There's even the reversible Valco Snap Ultra if you can get your hands on one, and that, with the optional Sport air-filled wheels, could work for you, too, even if not an all-terrain beast.