I have also seen teams throw the ball to the first baseman. If the batter rounds first she tags her. Once the batter stops at 1B return the ball to the circle and then she is subject to the look back rule. 1B needs to be aware of the runner at 3B and be prepared to throw home if she goes.
Throwing to 1st never activates the lookback rule and the runner at 3rd can just stand there or even increase their lead. Instead of the ball being 45 or so feet away, now the ball is almost 90' away at 1st base. And, nothing stops the batter/runner from just taking off for 2nd the instant F3 throws the ball back to the pitcher, or, running straight through 1st base toward the outfield and then making a wide turn to 2nd. Get the ball to the pitcher, the second the batter/runner touches first base the runner at 3rd must either advance or return to 3rd. You still have plenty of time to make a throw to 2nd for the tag and if the runner at 3rd does try to advance you still have a play on them also.