The fact you say, "...we don't need to know..." is an immediate disqualifier in your regard. Your mind is shut tight. If Oswald did leave the wedding ring behind, that bullhorns his involvement in the assassination. I do believe there was an escape plan which would have separated him from his family. So, he carries that rifle all the way across the 6th floor and THEN hides it? And then he jumps through several hoops to get to his boarding house and arm himself with yet another gun? And after all of this he just sits inside a theater that's showing a bad movie? But again, "....we don't need to know....".
\
Of course we don't need to know why Oswald did it. It would be nice if we could figure it out but not necessary in order to prove that he did. Proving motive is not something that is required to convict a person for murder. All that is necessary is to prove that the accused committed the act. We have ample proof of Oswald's guilt.
Oswald didn't duck into the theater to watch a bad movie. He did that to escape detection from the police who were looking for a cop killer. If not for an alert Johnny Brewer, it might have worked. He could have sat through the double feature until dark and then left with the other patrons. Who knows where he would have gone after that. Who cares. It is a moot point.
You seem skeptical that Oswald would carry the rifle across the sixth floor and then hide it. What was he supposed to do with it? Walk out the front door carrying the rifle on his shoulder. He wasn't stupid. He would have known the rifle would eventually be found whether he left it in the sniper's nest or hid it between rows of boxes. Perhaps he thought, hiding it as he did might by him a little more time to escape. We don't need to read Oswald's mind or second guess every decision he made to know he was the assassin. We have ample proof of that.
The difference between you and me is that most of what I believe is based on rock solid evidence with a few loose ends that are left to speculation, such as Oswald's motive or what his plan was once he left the TSBD. My own belief, which is pure speculation, is he had no plan. I think he was surprised he got away from the TSBD, but that's something we can never know nor do we need to. On the other hand, EVERRYTHING you believe is based on speculation, and then only after you invent one cockamamie excuse after another to ignore each and every piece of evidence that screams to us that Oswald was the assassin.
The assassination of JFK is not a mystery and never has been. Within the first four hours, the DPD believed they had their man and in roughly 12 hours, they had accumulated enough evidence to formally charge him. Since that time, the case against Oswald has only gotten stronger. The only question that remained after that was whether he had one or more accomplices. Two government investigations and legions of amateur sleuths looking for evidence of such accomplices over six decades, no one has found any evidence to identify any accomplices. The JFK conspiracy hobby is an exercise in futility that has been striking out over and over again for 62 years. If you haven't found evidence in that time of any accomplices, what makes you think you ever will.