If I have the attack of one of my pieces replaced, will the PD ability increase the replacement value? I know perplex won't work, but my reasoning is that both happen when the attack is made, not before.

Any thoughts?

Perplex is a separate action, so it would occur before the BME replace. This is true of a Perplex up or down.

PD is triggered by a ranged combat attack, so it would be triggered after the BME replace.

I'm not sure if it is triggered after or at the same time as Bat Enemy TA. I'd guess that it would be at the same time since you declare both TA's being used at the same time. In any case, I do agree that PD would indeed boost the AV of a Bat Enemy. If they occur at the same time, the active player always gets to choose the order in which they happen.

I thought the rule of thumb for replacements and modifiers that happen at the same time was "replace, then modify." Is that still true? (This would change things like Defend + Energy Shield if the active player got to choose.)

It is not only true, it is now in the rule book. Previously it was just an inofficial guideline.