Sprint to the end zone
 

On a long sweep to the opposite side, when do you stop “watching the trash” on the backside and start sprinting with the ball carrier to get to the end zone in time to signal the touchdown?

Assuming you're on a 5-man crew... never. Let the other Wing, and especially the BJ, do the sprinting. You, the R, and the U should be cleaning up behind the play. There's no need for 3 officials to cover the goal line and leave 2 officials to clean up 18-20 other players.

Right. Give a signal to the BJ and only the BJ signals the TD. If the runner goes out of bounds, get the spot and signal from behind.

4-man crew
 

Sorry...I'm talking on a 4-man crew...

I don't change my mechanics for 4-man. I let the runner pass and follow from behind -- best way to officiate the point of attack and the surrounding blocking.

In this case the other wing sprints and you do the best you can. You will not be straddling the goal line when the runner crosses, but that's OK.

Absolutely! Everyone has a circle they should be working. The farther away from the ball you are, the bigger the circle you should watch.

On a four man, you should cover the defender(s) closest to the ball carrier and OOB line on your side. The defender(s) are either going to foul, get fouled, tackle the runner, cause the runner to fumble or nothing if the runner scores. As far as the runner, you only need to worry if he steps on the OOB line.