What is hilarious are the number of replies that offer advice while evidently not paying any attention to the parameters Illinois hunters are bound by. Bottle neck cartridges have to have a case length no longer than 1.4 inches, .30 caliber or larger and be available as a factory load with published ballistics!
Straight walled cartridges are not limited as to length, but again, they must be available as a factory load with published ballistics!
I know the .445 Supermag is a real cartridge, but it is not currently offered in a factory load that I can find. Not that it matters. If one is going to fire a cartridge with that performance, there really is no reason not to go with the already well available .45-70 which can be tailored for pretty much every recoil level one would want to experience.
If one sticks to the 300 grain bullet for Illinois deer, you can load it to 1500 fps for a reasonably easy recoiling load similar to the .454 Casull, or you can push it to 1700 or 1800 fps for all the recoil fun your little heart desires.
It shades the .44 Mag considerable margin, not that anyone needs anything greater than the .44 mag for Illinois deer.
But, none of the factory bottle neck cartridges listed to date, fall within the parameters mentioned.
Dan