Chuck, another issue is that R’ Moshe wasn’t accepted as the main posek by most people. Yes, he was recognized as the posek hador by most. That doesn’t make him their Rav. Other people can argue on him, and you can go according to them. A competent Rav won’t argue on him without serious thought, but it can be done. If some local Rav of a shtiebel goes and argues on R’ Moshe zt”l, I’d say he was crazy. However, for a big posek, it can be done.
For example, R’ Shachter from YU is a huge authority when it comes to Eruvin. he happens to argue on R’ Moshe regarding a point in Eruvin. A Rav near me, who’s close to R’ Shachter, told me that when R’ Shachter gave his psak, he told this Rav that he didn’t sleep for 2 nights beforehand. He reviewed his point again and again. In the end, he didn’t really feel like he was arguing with R’ Moshe, he felt the circumstances had changed, and the psak shouldn’t apply any more. Even with that, he couldn’t sleep for 2 nights! That is the proper mindset for disagreeing with a posek such as R’ Moshe.