Question confuses me a little bit. Forget the circle or look back rule, I want the pitcher to receive the ball in the middle of the field. If anything is going on in the game they will be in the best position to react.
Added benefit in softball is the runners need to make a decision what they are doing or the play is over until the next pitch.
I do not know if this is the right strategy but DD’s HC has told pitchers never leave the circle unless they are making a play then get back into the circle. When in doubt the fielders are suppose to throw it to the pitcher. They are in the middle of the field so they are in a good position to either make a play or let it finish.
...With the ball in the circle after a batted ball, if the runners return to their bases the umpire will usually call time, which means you have a dead ball until the next pitch....