I love overly pedantic interpretations of the rules. It does say that participants in a battle take turns in combat. I wonder if that's enough to define that dead creatures can't act.
I believe dead creatures are objects rather than creatures but the problem is that the combat section is written in second person so it doesn't seem to matter if you're a creature or not. It simply says you take your turn.
Is that not the correct phrase? To your heart's content?