However, after working out the math, it appears that the optimal strategy against this one is actually a very nice one.

Of course, the same as in a game of chicken where your opponent precommits to defecting.

In infinite IPD:

• There are lots of probabilistic strategies your opponent can precommit to that prevent you from averaging CC (in this case: 3).
• If your opponent accepts any probabilistic precommitment from you without precommiting himself, you can maximise your score beyond CC.
• If you model your opponent as a probabilistic strategy, you accept any probabilistic precommitment from your opponent.

Point 2 may not be obvious, but follows straight from the payoff matrix.