i would check the scope and mounting system. I hate to tell you but most of the cheaper leupolds have issues. I had a buddy that had one and had to send it back because it was doing the same thing. It was on a 300wsm and wouldnt group just patterned but he said it shoots much better after he got it back.
Second I would look at the stock but I have a stevens 200 in a 243 and it shoots about 3/4 moa and it is still wearing the factory stock. If I was looking at a after market stock I would look at mcmillan or hs precision. of the top of my head I dont know if hs makes a stock for savages or not. Also getting an after market trigger will help alot. I shoot 2lb triggers on my hunting rifles but thats just me. Some of the people who shoot my guns at deer or what not hate them because they simply were not expacting the gun to go off when it did. that will be somthing you will have to find out for your self.
I dont know who ever came up with the imaganary word of "Over Gunned"