Thrown Bat Penalty

 
In the first inning, #17 of the home team flies out to the center fielder. However, just after #17 hit the pitch, he accidentally threw his bat and the bat hit the catcher in the head and the umpire in the chest. After the play concludes, the plate umpire issues a warning to the coach of the home team.
 
In the 6th inning, with the bases loaded and two outs, #34 of the home team hits a bases-clearing double. After the 3 runs score and #34 is standing on 2nd base, the plate umpire calls "time" and notifies the home team head coach that #34 has carelessly thrown his bat and hit the catcher. Is there a penalty for #34's thrown bat? What action should be taken by the umpires? Do the runs score? Is the inning over?
 
Call
There are rule NF differences between: A) A carelessly thrown bat, B) An intentionally thrown bat, and C) A bat that is thrown and interferes with a defensive player attempting to make a play. The most common thrown bat is one that is accidentally released by the batter (referred to as a carelessly thrown bat). On the first carelessly thrown bat, a team warning is issued. On the next thrown bat by a team that has already been warned results in the offender being ejected (but not called out).

In the play below, in NF, the home team was warned, so #34 will be ejected (restricted to the bench) and replaced with a legal substitution. The runs driven in by #34 score and the inning continues with #34's substitute on 2nd base.