Like the others have said, I am not calling time until the action has stopped. If the playing action (advance of BR/R1 has stopped, with no apparent idea of doing anything else), then I will call time.
The catcher in possession of the ball in the circle means nothing as far as the LBR goes. So, there is no violation of the LBR in your second situation.
Now then, what fields are you on where there is a mound in softball?