what if C/D provides a greater net payoff than C/C

The Prisoner's Dilemma is technically defined as requiring that this not be the case, precisely so that one doesn't ahve to consider the case (in iterated games) where the players agree to take turns cooperating and defecting. You are considering a related but not identical game. Which is of course totally fine, just saying.

If you allow C/D to have a higher total than CC, then it seems there is a meta-game in coordinating the taking-turns - "cooperating" in the meta-game takes the form of defecting only when it's your turn. Then, the players maximise both their individual scores and the group score by meta-cooperating.