Out of Play Throw from Infield

 
With 1 out and runners on third base (R3) and first base (R1), R1 is stealing on the pitch. The batter hits a line drive right at the second baseman, which is caught for the second out of the inning. The second baseman has an easy opportunity for an inning-ending double play on R1 at 1st base, but he air-mails his throw past the first baseman and out of play. R1 was half-way between first and second base (heading back towards first base) when the ball went out of play. The field umpire directs R1 to third base and R3 to home. R1 goes to 2nd base and then 3rd base, while R3 goes home.

The defensive coach feels that this award is too generous (after all, the ball never left the infield!). He feels that R1 should get two bases -- the base he was heading towards (first base) and then second base. What do the umpires do?

Extra Credit: The home plate umpire (me) sees an opportunity to end the inning without another pitch being thrown, but I will need some action by the defense. What action would that be? If we can end this inning without the ball even being put in play, does R3's run count?

Call
While the ball never did leave the infield, the award is two bases -- so R1 was properly awarded third base, while R3 scores.

Even on dead-ball base awards, runners must properly complete their base running responsibilities.

R1 did not properly tag-up at first base before advancing on his dead-ball award. R1 is at risk of being called out for not properly tagging up. If properly appealed by the defense, R1 can be called out. This is a timing play. If R1 is called out on appeal after R3 touches home on his award, R3's run counts.

As someone pointed out in a reply, if R3 also did not properly tag up at third base, his advance can also can be appealed in order to negate his run.