I don't think the one excludes the other. To explain:
Benefit of the doubt goes to the shooter. So a hit on the wrong type target is counted as a miss, not a P -- rather than try to determine whether it was an intent to hit the right target that went astray, or a brain glitch that put the shot on the wrong target, we just call it a miss and move on. Only the shooter knows for certain.
Benefit of the doubt.
There is enough vagueness in the OP to let anyone support their position. Was the first shot on the far side of the stage from the KDs, was it something that was more likely an AD, except the shooter was in the process of aiming and therefore gets a pass, was the target on the other side of the stage where the shooter would have had to move to engage it? Can't tell.
So if the shooter has an 'engage 'till down' description, and wants to claim his first wild shot was really the re-engagement, that's on him. If he sweeps five straight, then it's likely he would have swept six straight as well.
But if there was a required order of engagement in the stage description, then sure -- the 'make-up' shot for the failed target would have to be in the correct sequence, whether first, last, or middle. Otherwise, it's not re-engaging that specific target at the appropriate point in the string.
Does that mean some shooters would work the system to their advantage? Sure. But an SHB that could keep anyone from slipping through a loose gate would get pretty big.