Catch-and-Carry with Runners Tagging Up

 
With one out and runners on second base (R2) and third base (R3). the batter hits a foul pop up down the left field line. Both R2 and R3 return to their base to tag up. The left fielder catches the foul pop-up and then he ends up running out of play into dead ball territory. Both R2 and R3 properly tag up and head for their next base. The left fielder then returns to live ball territory, throws to 3rd base -- where R2 is tagged out (for the 3rd out of the inning). R2 was tagged out at 3rd base just before R3 touched home.  
 
An argument breaks out between the coaches about whether the run should count or not.
 
The umpires have a lot to sort out here... now what?
 
Call
In NF, when a defensive player carries a live ball into dead ball territory, the ball
is immediately dead and the base runners are awarded one base.
 
In the play below, the batter is out on the catch, but the ball becomes dead when the left fielder enters dead ball territory with the ball. R3 is awarded home and R2 is awarded third base.