Old Abe there's a place up in Lena called Muel's Sled Salvage , call or text 815-821-2409. Not far from you and the first pic on his facebook has a red Formula 500 in it! Good Luck!
Sorry, I should have gotten back to you sooner on this. The main issue with salvage yards is that a lot of them won't pull the part for you. Bam's Toys in Oxford Wi. has a ton of parts but you may have to pull it.
As REVERUP mentioned, I'm finding myself buying more and more stuff from ebay. Prices as usually good, shipping is free most of the time, and it saves me a lot of driving. Since you know exactly what you're looking for, you should be able to find one at a reasonable price.
I googled "2001 Ski Doo Formula 500 Carb" and got four hits from ebay varying in price from about $50 - $90. Some of these are listed for different years but may fit. I'm trying to find out exactly what size your engine takes. You could probably message the seller, they usually respond fairly quickly. This is a link to one that was listed as a new carb but may be a Chinese knock-off. There are others to pick from if there's any question about it's quality:
Hudons Powersports is a Beta Motorcycle, and Kymco Dealership. Its the World's Largest Sled Salvage Shop. It carries new and used snowmobile parts for Polaris, KYMCO, Bennche, Yamaha, Kawasaki, & more. A family owned business that loves to ride motocross, dirtbikes, ATV and snowmobiles.
If it is a Formula 500F, it should take a Mikuni VM34 carbs (I assume it has two). Not sure what jetting yours would need but the carb is pretty common and any VM34 should work. with proper jetting.