Whether one considers (A) the same or different after it has been restored to its original mathematical relations (B), is purely a matter of cognitive estimation (opinion). Therefore, to say that any (B) is an “original,” is itself just an idea.
You have no opinion on it, I see. It could be the same or it could be different. As such you are treating the problem as if it were about any kind of difference. You are a different person than you were yesterday or you can be the same person you were yesterday, all a matter of opinion, as you say. Chicago is different today than yesterday, or it is the same as yesterday, it's just a matter of opinion, an idea in someone's head. You don't seem to be getting what the paradox is about. The paradox specifically talks about replacement of parts. What is the impact of replacing a part? Is there an important distinction between replacing one or a number of parts and replacing every part? Suppose it were possible to take two ships, one that was the Ship of Theseus, while the other was some ship that looked somewhat like it, and could be fitted in such a way that the parts that would be used to replace those on the Ship of Theseus could instead be used to remake it to be identical with the Ship of Theseus. Now we have two identical ships, right? Is it then a matter of opinion whether the untouched ship is still the Ship of Theseus, or should we now think the remade ship is the Ship of Theseus. One might imagine there is a confusion over which one it is if we weren't told, but, like the game with three cups that all look alike, we should all agree that after shuffling them, each of their identities remain untouched. If originally labelled A, B, C as they are lined up, at the end of it, they would be in some rearrangement of those labels.
This being the case, it should call attention to the issue of what it means to be the same thing, when undergoing a change by replacing parts of some object. The idea here is that the parts are identical in everyday to the original. There is no important distinction between the part being replaced and the replacement part. One could ask the same question about the part, if it, too, consists of parts. We could take the paradox all the way down to molecules, or atoms or ions, if that were possible.
One part of the paradox then is whether or not the Ship of Theseus is more than the sum of its parts. Is there something about it that isn't affected by replacing any or all of its parts, that if some other object were composed of the same identical parts would be left out of it? This is what used to be thought of as the object's substance, one that in us, we identify with our inner self, which presumably remains untouched if any of our parts are replaced.