Piccadilly's recipe is simply a very sweet carrot custard. In your situation, I would make about 6 full chafers of carrot stuff.

Here are some quantity guidelines for 250 people. I have to say I would do this in batches-

62 1/2 lbs carrots, cooked
8-16 cups butter, melted; may use part oil
10 dozen eggs, beaten fluffy
6 to 10 1/2 cups flour- this depends on the wetness of the carrots
2/3 cup to 1 1/2 cups baking powder- smaller amount for less flour, larger for full amount
8 quarts sugar (MANY cooks use half this)
5 cups brown sugar
3 1/2 tablespoons cinnamon
1/2 cup vanilla extract

May top cooked pudding with:
1/2 cup and 2 tablespoons and 1 teaspoon confectioners' sugar for dusting