One trip my daughter was going through a grilled cheese thing, she was about 5 at the time. We found that you could ask most cs places that have a grill (burgers on the menu) to make you one.
LOL, this is what I was going to say. They have bread, they have cheese... voila. How hard can it be? This is one of those situations where it doesn't hurt to ask. What's the worst that can happen... they say no.
My son said he had the best grilled cheese sandwich ever (triple decker) at Ohana for dinner. I know it is not CS but if you are there for TS -- it is good.