At the risk of driving off the road into the weeds, you bring up the most important issue with shooting the .22 High Power in these modern times. First of all, the old 1899 Savage HP's were rifled with a 1-12” rate of twist (ROT). That ROT is barely enough to stabilize the long heavy bullets which the cartridge is built around. The current commonly available bullet, the .227 70 grain spire point from Hornady, is too long to be well stabilized. As we know, it's the length of the bullet that matters in this instance, not weight, and the Hornady bullet is too long at .850". I found that trimming them to .800” length or shorter improves accuracy dramatically. I speculate that this Hornady bullet was intended for the European market and their fast twist 5.6x52R stalking rifles. On the plus side, they are abundant and cheap.

The original factory 70 gr. loadings used round nosed or semi-spitzer shaped bullets that were just short enough to stabilize. The current Norma and Sellier&Bellot  loads use bullets that are similar, and also work well. Speer used to make a short enough semi-spitzer 70 grainer that was a dream- but is now discontinued. If you stumble onto any old Sisk bullets, grab them as they were wonderful too. Buffalo Arms sells some lightweight and hence short enough bullets but I suspect them to be not heavily constructed for deer hunting. (They do shoot well in my experience though.)

Another note regarding cases: making them out of .25/35's or .30/30's is the way to go, but a PIA. The European HiPowers (5.6x52R) are nominally ok to use, but something was lost in the translation from U.S. to metric dimensions and as a result are a tad bit small in their head diameters. This combined with some sloppy chamber dimensions can make for short case life- especially if said brass is gotten by firing factory loads. Those Euro loads are hotter than old U.S. factory loads, which does nothing for initial case life too.

I found that staying at 25 grains of 3031 or 26 grains 4895, or less, with a 70 gr. bullet, makes for a pleasant medium load that is accurate, gives good case life, and kills deer with alacrity.