Not sure if legal in Illinois, but if Iowa was single shot only I would definitely be 100% smokeless muzzleloader. Our law states .45 caliber or larger and loaded from muzzle.
My entire family shoots a lot of prs style matches. I had my gunsmith do a savage prefit with a Hankins ignition. I have an 11 year old and an 8 year old daughter. The gun has a very aggressive muzzle brake on it to reduce recoil. We hunt with electronic muffs. With 65 grains of 4198 and a 300 grain bullet the thing is a hammer. It kicks about like a 20 gauge slug gun. My 11 year old daughter is 5 ft tall and weighs 75 lbs. She handles it no problem and used it to kill 3 does during youth season this year already. My 8 year old needs the load reduced to 35 grains of 4759 which still pushes the 300 grain bullet at 2050 fps. The deer still look like they were hit with a Mack truck and the recoil is nothing. (She weighs 55 lbs and loves to shoot it) The bullets expand really well and the gun will shoot sub 1/2 minute for 3 shots at distances I don't want to post. Iowa allows muzzleloaders during all firearms seasons.
Last year the girls killed a 4 year old 150" 9 point and a 5 year old 145" 8 point with a 21" inside spread. Both of those shots were around 190 yards with the reduced load. Several doe kills from 80 yards to 303 yards with the reduced load. Obviously, you need exposed turrets and the ability to call wind to make some of the longer shots, but the gun is capable.
We have a Ruger American in 350L. It is accurate enough, but it feeds like shit and the results with 180 Winchester factory have been pretty anemic. One buck at about 40 feet on the point of the shoulder DRT. Everything else has been broadside and low in the lungs or heart. They bleed but entry and exit are pinky size and they don't act like it's much trauma.