There are likely a number of things going on here. Yes the recoil pad will help. My suggestion is to get a different rifle. You'd be just fine with a 7mm-08, .308, .270, heck even a .243 Win can take game out to 400 yards.

So my suggestion, chalk it up as a mistake and get another rifle. If you're hard headed and don't want to go this route, then yes get a recoil pad, I'd strongly recommend a Decelerator instead of the limbsaver. If that doesn't help then I'd suggests a couple of rags in the shoulder area under your shirt.

I'd stay away from a lead sled as I've seen many of them not hit where you're aiming once you put the rifle to your shoulder. I don't own one but have seem many at the range in use.

Good Luck, I hope you decide to get another rifle.

Tom