You won't like the answer, but when I had our first child, I switched back to glasses, precisely because of the ability to quickly transition from awake to napping when the baby slept. They're old enough now that I could probably switch back, but I don't think contacts are viable for the quick napping.

If it's just the protein buildup on the lens, you might try taking out set A, napping quickly, and inserting a fresh set B of lenses while set A continues to clean in the solution. They're cheap enough to try anyway.