I think that to argue that morality is subjective essentially is to argue that morality don't exist. You can easily argue that people have personal morals, which they look to to guide them in their own sense of right and wrong; you would be hard pressed to deny that people have these thoughts. However, when you say "morality" out of the context of a specific person, it implies Morality with a capitol M, a sort of universal scale of good/evil, a.k.a. objective morals. To argue against objective morality is to argue against Morality.

You say that reality is to judge which of the two people with different moral inclinations is correct, but in doing so you are assuming that it is possible for one to be "correct" about morals, and that morals are intrinsically tied into the nature of reality. To me it sounds like you are assuming your answer to the question before you make the argument. One would need to prove that morals are bound to the nature of reality (physics, one might call it) in order to assert that there can be universally "correct" morals. So far as I can tell, all manifestations of "morals" come from the thoughts of subjective beings, not inscribed somewhere in the laws of physics.

On a similar note, you say that the subjectivity of passing through walls is of equal Truth value to the subjectivity of morals, but passing through walls seems to be much more questioning the nature of physics in a very direct way, whereas we have yet to prove such a connection between morals and physics. In this case, whether or not one truly can walk through walls is objective, but whether or not one thinks they can is subjective. The only reason we label the person who claims to be capable of such feats as "wrong" is because an overwhelming majority of people subjectively think it is impossible, based on their own subjective experiences with the nature of reality.