I have never been able to get those SP's to shoot very good in auto loading rifles with NATO chambers.
The Nosler Ballistic Tip in 55 grain seems to not only tolerate jump, but thrives as the largest chamber rifle i own shoots them sub 1/2 MOA.
Another bullet that shoots well in even bad barrels is the Sierra #1390. You have to make sure you are not jamming the lands on that one though.
I like how you are going to change bullets instead of many different powders. That is the way to go.