I acquired a Weaver K4_W to mount on my pre-64 Winchester 70 300 H&H mag. Using Leupold Low QR rings and bases. The scope has about 2 1/4 turns of vertical adjustment. I got it sighted OK windage wise. but couldn't get closer than 4" low at 50 yards.

Any ideas? different rings/bases, shims, etc?

Look for the mounts with 10-20MOA inclination built in.

George

The solution to this one is so easy that I always marvel that it comes up over and over and seems so elusive.

Simply remove the scope from the rings and place one, or possibly two, thicknesses of black plastic electrical tape on the inside bottom half of your rear ring underneath the scope tube, thus increasing the coincidence of the scope's line of sight with that of the bore. If you have a gun that refuses to shoot low enough, simply do the opposite by placing the tape on the inside of the front ring underneath the scope tube.

"Purists" will cry that this will put your scope tube into a bind. Hogwash. The windage adjustments on many scope mounts create a MUCH greater misalignment than is created by the soft electrical tape and your scope will not suffer "ring marks" or other signs of ring misalignment. Besides, if your scope is as far off of the line of the bore as it appears, it is likely a result of rings being slightly mismatched, meaning you already have a ring misalignment problem and the bushing will help resolve it.

I've had a Sako with rings bushed this way for over 45 years. Whenever I check its zero (about every five years, these days) it is always exactly where I left it a half-decade previously. And the same 45 year-old Leupold Vari-X II still sits in those bushed rings.