I suggest you will not achieve the results you want until you improve the gun you are using.
A better barrel and a better action/trigger will make a big difference. If you really want to shoot one hole targets on a consistent basis, a custom action and barrel is the answer. In addition, a more accurate rifle is needed to actually see the results of changing loads or loading techniques.
Don't spend any more money on a factory rifle, save up for a custom action, bedded in a stock, a Krieger, Brux, or Bartlien or other big name barrel and a good trigger.
You will also need a good front rest (with a stop to repeatably locate the front of the stock) and good rear bag.
I suggest that 6mmBR is the easiest to load, high accuracy cartridge. 30 gr of Varget with a Berger 105 hybrid is a starting point, and may well produce your one holer. Cases seem to last forever. You can run standard necks without neck turning.
I suggest you avoid the 6PPC. While super accurate, to get that accuracy, it runs at such high pressure that the cases don't last very long before the primers will be very loose. They require fireforming from a 220 Russian (or hydroforming), and require neck turning.
While you are saving up for a new rifle, I suggest your Savage in 6BR is your best bet for now, depending on the twist rate. The 105 Berger needs an 8 twist or faster, if yours is slower, you need to use a lighter bullet. It can be equipped with a name brand barrel ( yes I know I said don't spend any money on it) but it may do the job as is with the factory barrel as you polish your skills.
Perfect your shooting skills, ie, placement of gun on bags being repeatable, hold, ie free recoil or actually holding the rifle in a repeatable manner, careful, repeatable trigger pull, and a consistent sight picture.
I am seriously considering go back to 6BR again as most of the people are saying. I may didn't explained myself very well but I sold the Savage, I actually have a Bergara Premier