Game Situation: Outfielder Throws Out of Play


 
With runners on 2nd and 1st, the pitcher attempts to pick-off the runner at 2nd. The throw sails into center field and the runner at 2nd heads to 3rd, but the runner at 1st remains on 1st base. The center fielder retrieves the ball, fires it near third, but well out of play. The plate umpire calls "time" but now where do you place the runners?
 
Call
This is a two-base award for all runners -- so the runner on 2nd is awarded home and the runner on 1st is awarded 3rd. The plate umpire calls "time" when the ball goes out of play and the base umpire points one runner to home and the other to 3rd base.

Follow-up question: Since the ball is dead when the runners are awarded their bases, is there any problem if the runner near 1st base cuts across the diamond to his awarded base (3rd base)?