You think well, and all three of the mentioned prams are quite capable of handling parks and rougher terrain, as they are quality and sturdy. I, however, am doubting that compactness / 'not too bulky' requirement as all three are actually quite large, especially when folded, which you should take into account. I personally would go for the Fox 3 out of these three, as it is a little better, folded frame-wise, and also it is lighter and overall the best value for mones.
A three-wheeler like the Baby Jogger City Mini GT2 would definitely be a smaller, more practical choice for what you are searching for, though you will lose the reversible seat option. A bassinet and the Cybex Cloud Z car seat can be attached to it, though, and after checking if in your country the accessories and adapters are available, it should work very well for you (except for that reversibility).
Definitely think about whether a reversible seat is something you need, and also check smaller stroller models like Cybex Mios, which is small-wheeled but sturdy, and for parks and occasional grass could work... as the size difference is considerable. Or the new Nuna Triv Next which had a bump in size in the rear wheels. Hope I helped!