I was going to mention catering like Angela did, unless you just let the food run out til whenever it was planned to put the rest out, maybe just having a dinner would be better? I don't know if catering would cost you more or what the situation with cooks, etc. would be to even have some people volunteer to do it.
Unless you had a specific table, IF you catered, no non-food tickets. And if they did want something, maybe have some extras of an appetizer or something, so if they wanted some food, you could charge them for it, it would be less than a full meal maybe, but you make something off it, and are not running out of food. Also, maybe you could do bread sticks or something cheap at the tables, or whatever they sit at...
Most fundraisers I've heard of, they just offer a dinner.
Maybe you could do a salad bar where people could just go up and get food too? Or that could be like the "freebie" part of a non-food ticket. I haven't done a fundraiser so I don't know, just some ideas.