You are correct, the lunch menu at the Marketplace only offer the PB&J or turkey sandwich for kids for a CS lunch. However, Hurricane Hannah's is also open for lunch and has loads of things kids like for CS lunches.
As far as CS breakfast options, we are very limited indeed -- a few items at the Marketplace is pretty much it. There is also the Bakery across the way at the Boardwalk but that isn't much better. I also suggest to guests that they get an early start at the parks and eat their CS breakfast there if that is what they are looking for. The Mickey Waffles are in the buffets at the Cape May and at the Captain's Grill but they are not CS. Last summer they did a "test" and had a nice CS breakfast at Beaches & Cream. It went over very well but it was only a test. We are all hoping they bring it back permanently.
If you are on the dining plan, I always suggest that you use your CS for an early lunch at the parks and use your table service for dinner. It seems you get the most out of the dining plan money wise if you use your meals that way. When we are using the dining plan, we grab a quick muffin or cereal in the morning (pay for it or use our snack option), get a large early lunch at the parks with our counter service (our favorite is Blame Tree BQ at DAK) and use the table service for a dinner. When you use your table service for a character breakfast at around $18-23 a pop, it's like tearing up twenty dollar bills. That same table service can be used for dinner at Teppan Edo or somewhere similar and it would cost you $40+ for that meal. If I want to do a character breakfast, I pay for it with cash.
You can refill your mugs out by the pool at Beaches & Cream and also at the Marketplace.
I agree we are lacking for CS breakfast options, but we are a super nice friendly resort and I personally think SAB makes up for the lack of CS breakfasts. And remember, we are only a 4 minute walk to Epcot where you can get a nice CS breakfast at Sunshine Seasons after you get your fastpass to Soarin.