This came up at our state rules meeting last night:
3 whistle NFHS. Ball goes out of bounds on the Center's line in the backcourt. Which official administers the ensuing throw-in?
A. Old Lead (New Trail), old center becomes new Lead
B. Old Center (New Trail), old Trail becomes new Lead
C. Old Trail (New Trail), old Center becomes new Lead, old Lead becomes new Center
D. Nearest Howler Monkey (they all want to "officiate" so why not make them do their part)

Hope this makes sense. Our state wants us to choose B. The majority of us would rather go with A and bump the old Center down the floor.

I'm not quite sure I follwed the play and the options, but if the throw in will be by A and the ball is "in" A's backcourt, then bump-and-run. That woul dbe your option B, I think

If the throw in will be by A the the ball is "in" B's backcourt (e.g., B threw it away while advancing up the court), then the official responsible for that line (C in your example) throws it in and the other officials balance the court. That would be your option A, I think.

All throw-ins in the backcourt will be handled by the T...so the T should come over, C bumps down to L, and the L slides out to far-side C...

If you are talking about the play where the ball has obtained front court status, and is then knocked out of bounds in the back court by B....thus A retaining the ball with a throw in from their back court, the Old C will administer the throw in. Once the ball gets to the front court, the rule of T handing all back court throw ins goes out the door and the official whose line the throw in will occur on will handle it.