STC on simultaneous possession Q

[kentref]

This play happened in a youth game with a 3 man crew. I probably should have added that in at the start, but I am more interested in what the linesman should have done in this situation, (regardless of the crew size).

For this type of play does it make any sense for the linesman (who sees joint possession), to drop a beanbag at the yardline where he sees the joint possession? He then continues to officiate and confers with the umpire when the play's over. Let's say that's what happened, and after the linesman and umpire confer, they decide it was joint possession. You move the ball back to yardline marked by the beanbag and it remains A's ball. Now, do you put time back on the clock?

Note: I don't like to see the umpire determining when the play's over (i.e., determining that forward progress was stopped), and that's pretty much what I'm conceding in the previous paragraph. However, in this situation, if it's the linesman that eventually blows his whistle (after he's dropped his beanbag earlier), that just seems awkward, since he should have stopped the play at the joint possession spot. Thoughts?