I wouldn't play to much with it. I assume you dropped the trigger down. Beyond that, an aftermarket stock is not going to do much better. Even though the savage stock is a flimbsy piece of trash. It is thick and sturdy where it counts, at the action. If you want to shrink the groups, may try a piece of foam under the barrel directly above the sling stud. Just in case the bipod is able to bend the forearm slightly to contact the barrel. Make sure every time you break it down the screws are tightened back up to the same degree. If you plan to reload neck size only. You should get that little gent to one hole without any more money at all.
Blessings