We finally put up a gate to keep Zack out of the cat food, water, and litter. The cat can go and has been going in and out under the gate. He has to squeeze a little but he doesn't seem to mind.
On the way back from the park, Zack was very insistent that he nurse, so we nursed in the carrier, which we haven't done in months. He fell asleep, and more importantly stayed asleep through the transition from outside to inside when we got home. He's still sleep nursing in there.