Yes, in our home game (be they ALPHA STRIKE or TOTAL WARFARE) we go with the following for attack phase:
TODD declares Mech A fires at Mech 3, rolls his attacks, and applies all damage.
DUNCAN declares Mech C will attack Mech 3, rolls all attacks, applies all damage, gets a Head Shot, and destroys Mech 3.
DAN declares Mech B will then attack Mech 2 (Mech 3 was the better shot but now dead, so takes the crappier target), rolls and applies all damage.
For Myself, I then say, Hmmm...Well, Mech 2 is dead this turn, so he will attack Mech A with everything (which on a normal round would have put it to 23 heat, but...he's dying Jim!), roll attack, applies damage, get 2 engine crits, which puts mech a at now +10 heat.
Again, this method puts more Omniscient Knowledge into the pilots, but it also stops a lot of "Oh...I was attacking that guy, but now he's dead, guess I need a new target next round." thumb twiddling.