We've stayed at the Polynesian twice and love it. Captain Cook's is basically a snack bar with a couple of refrigerator cases; it doesn't offer the variety of the food courts at the other resorts.(On the other hand, the other resorts don't have 'Ohana and Kona; more on that in a moment).
One thing we did to save time in the morning was get breakfast at Captain Cook's the night before. After the girls would go to bed, I'd wander over to Captain Cook's, get cereal, milk, fruit, bowls, and spoons and bring them back to the room. I'd put the milk in the ice bucket and then cover it with ice; that kept it just fine until the morning. In the morning we'd have a quick bowl of cereal and head on out without spending time in line or finding a seat or anything like that.
Turns out this also saved money (compared to getting breakfast at a restaurant). This cost me about $7.00 a night, but we didn't have to get a refrigerator or hump a suitcase of food along with us. (There's only three of us and we flew; if there were seven of us and we were driving it would cost $18 or so and I'd have a completely different attitude toward bringing my own food).
One more thing.... save money and time to have at least one breakfast at Kona.... it's GREAT! I promise, you'll thank me.
Good luck and have fun,
Kevin