Does exchanging a dead card count as a move for loss of a card?
Based on the wording, Dead Card exchange is basically a free action that you can do before taking your normal turn. Losing your draw is a result of the next player placing and drawing, which is effectively them finishing their turn. This strongly implies that you have until the next player finishes their turn to draw your new card.

In the scenario above, A is a 100% right to draw a card because B hasn't moved yet. Generalized, though, is technically vague but I think what I've said is the intentions of the rule.