I think the rule on blocking the plate is that you may cover some of it so long as the runner has a direct path to part of the plate. Blocking the front while leaving the back half is permissible, I think.
This is what I found--perfectly unclear and subject to interpretation.
(2) Unless the catcher is in possession of the ball, the catcher cannot block the pathway of the runner as he is attempting to score. If, in the judgment of the Umpire, the catcher without possession of the ball blocks the pathway of the runner, the Umpire shall call or signal the runner safe.
Notwithstanding the above, it shall not be considered a violation of this Rule 7.13 if the catcher blocks the pathway of the runner in order to field a throw, and the Umpire determines that the catcher could not have fielded the ball without blocking the pathway of the runner and that contact with the runner was unavoidable.