RR's bulletin makes it pretty clear. We don't care about the ball. It is a centerline through the middle of the field.
Actually, the "north-south" line is anywhere between the sidelines, and it is only used to determine whether or not the block is parallel to it, or at some angle to either side. It has no bearing on determining which sideline is a player's "adjacent" sideline. In fact, it doesn't even exist until a block is thrown.
As for determining the adjacent sideline, RR's bulletin on BBW says, " ...the sideline
closer to a player at the snap determines the direction he is allowed to block low." So, the position of the ball has nothing to do with it. If you are closer to the right sideline than the left sideline (at the snap), then the right sideline is your adjacent sideline. That being the case, then, yeah, being on one side or the other of the centerline of the field is going to govern.
My heartburn with the bulletin definition is that it is possible for a lineman or a back to be nearer to the sideline on the opposite side of the formation than the one on his side of the formation, AND be more than 7 yards from the middle lineman or outside the tackle box, respectively. Unlikely, yes - because it it would require an unbalanced formation toward a sideline from an inbounds line - but possible. That would mean that (technically) such a player(s) could legally BBW back torward the formation. I doubt that this is intended, but that's a conclusion that
could be drawn from RR's bulletin. Fortunatley, the
rules don't really define which is the adjacent sideline. So, it will be easy for RR to issue a bulletin that re-defines the adjacent sideline as being the one to the same side of the middle lineman as the player. And, I believe
that is what is intended.