RE: Need to find a .22 that shoots S,L,LR
Any lever action will do it, henry or marlin take your pick. Most bolt actions should do it as well, even if they are clip fed, but a tube might be better.
Are you wanting to mix ammo or just be able to shoot different length shells when you want to? Any bolt action or auto can be loaded manually. I used to shoot shorts out of my model 60 all the time. It just won't cycle the action is all.
I really think a nice lever gun is the way to go for what you want though. I owned a henry and it was real nice for the money. My dad has had a Marlin for ever (40 plus years) and it still shoots great, it's the gun I learned to shoot with.
Paul