1 or 2 T's?

Had a situation (similar to what I'm posting here, but a little different) last night that got my partner and I to talking afterwards. Team A is shooting 1 and 1. Ball is bounced to the free thrower A1 for his shot. Horn sounds just as the kid gets the ball, and trail looks over to the table and see Team A's sub A6 running in while his teammate has the ball to shoot the 1 and 1.

Our discussion led us to this answer to the situation: T on A6 for entering the game without being beckoned, team T on A for having 6 on the floor during a live ball. A1 shoots his 1 and 1 with the lane cleared, then administer B's free throws for the T's.

I kept reading the rule book and casebook last night, but couldn't find anything definitive that would "disagree" with how we would have ruled on it.

Of course, partner and I agreed that we PRAY this never happens to us but you never know in some of these sub-varsity games.