I have one of those for a Remington 700. The top of the stock is rounded, rest easy there. They are a real good stock, heavy too. If you want to use it for a carrying rifle, I would look else where, but if you want it for PD's, bench shooting of any kind, they are the bee's knees. Even though it has an aluminum block - which stabilizes the stock/action for sure, you may still want to skim coat between the action and the stock and put a little right behind the recoil lug. You may not need to either. I would get it and give it a try, then decide if you want to do that. Since you are taking about a Stevens rifle (?), be sure to get a stock that fits your action. If it is an older stagger feed magazine it will take one and if it is the newer inline feed magazine it will take another. I just reread your post and it looks like you are all over the inline feed -sorry. Get it, you will like it unless you are going to be lugging it around a whole lot. Good Luck and Good Shooting