I've done some quantity cooking, and I've noticed that people never seem to eat as much as you expect them to.
So - the recipe says serves 3 as entree; I figure that means about 8 side portions, depending on what else you're serving with it.
Allowing for the people who won't have any, your 250 goes down to about 220±.
This rounds to about 28 times the original
So (If I've managed to figure this correctly)
7 pounds Butter
3 1/2 gallons Cream
3 1/2 pounds Parmesan Cheese
21 pounds Fettuccine (can probably get by with 20 )
If you have the storage, I'd recommend multiplying by no more than 4 and making multiple batches. Some things don't take to doubling or more well.
Penne is 'heavier' than fettuccini, so just as much weightwise doesn't look like as much platewise. Noodles fluff up on the plate more than a larger shape, resulting in perceived larger portions. (At least in my limited experience )
Hoping all goes well, and that some of the more experience people chime in to help, too