Currently the aim points are already adjusted per game. Light Guns are notoriously unprecise, its not surprising that you have to adjust your aim point even during a game.
So what you are experiencing is only the tip of the iceberg.
The Pause after rewind is intentional, so that you can rewind multiple times. IIRC the menu is indeed the only way to exit here by default (ran out of options). But you can remap if you prefer a different setup.