I understand the sentence as follows: "Concerning map B, it is the card he made north and south not being top and bottom and put it left and right."
My main issue so far is that 上下ではなく has no connector to it like て form. The fact that 左右に置いて is て form doesn't make things easier. I could imagine that 南北を上下ではなく...作った form one attribute for もの. 左右に置いて could be, well, another addition, an adverbial phrase maybe, I struggle determining the syntactical function. "He made north and south not being top and bottom and put it left and right" I also have problems with the semantics of て form in this context. simply chaining it kind of still works, but I feel like it should have an adversative meaning: "He made north and south not being top and bottom, but put it left and right." But I haven't learned so far that て form would be allowed to use this meaning.