Timing Play on Tag-Up Appeal

 
With one out and runners on second (R2) and third (R3), the batter flies out to right field for the second out of the inning. R3 properly returned to third base, properly tagged up, and scored. However, R2 did NOT properly return to second base before advancing to third base on the fly out.
 
The defense then calls "time" and properly appeals that R2 advanced without properly tagging up. The umpires agree and call R2 out for the last out of the inning. The offensive coach reminds the umpire that the last out of the inning was called after R3 scored, so the run should count. 
 
The defensive coach reminds the umpire that R2 was forced to return to second base and runs do not count if the last out of the inning is a force out.
 
What do the umpires do now?
 
Call
A force play is a play that a runner loses his right to the base he occupies and is forced to advance because the batter has become a batter-runner (NF 2-29-3).
 
In the situation below, when the batter flew out, any force was removed. R2 was not forced to return to second base. R2 was required to properly return and tag-up or else be at risk of being called out if properly appealed. 

Since this is a timing play, R3's run counts.