Model 70 .375 Safari Express Shooting Low

I have the same rifle and Warne bases/rings. It sure looks like you have the right setup. Not sure if it was this rifle or one of my other M70's, but I had the same problem. This may not be what you want to hear, but it may be the actual problem. The problem may be that your scope just doesn't have that much vertical adjustment and you need another scope with more. That's how I resolved the issue.

The concern I'd have with adding more "shims" to the rear base is you're moving the rear ring further and further out of alignment with the front. This is going to put stress on your scope at some point.
Actually, by shimming the rear base he should be bringing it more and more INTO alignment with the front base, hence REDUCING the stress on misaligned rings and scope tube.
 
Good eye, I am on round #2 with tally bases, had their customer support help me with some bases that fit my leupold compact , different size bases for different types scopes
But those Warne bases have slots enough in the front base for the ring to be moved back away from the bell. This was a problem for me when I changed scopes on my Springfield 03A3 a few years ago. The holes for front base were off center and the rear base attaches to the military rear sight dovetail which suffered from lack of uniformity during wartime production. My rear sight dovetail is higher than it should be. So when I had two piece Weaver bases on the rifle, some creative shimming was required for forward base to deal with turret runout both elevation and windage. Then when I changed scopes, the new one had a short tube that wouldn't give proper eye relief with ring mounted behind the bell. So I went with a one piece base with multiple ring slots (which cured the windage runout) and shimmed the front to raise it. If I'd been thinking properly, I should have filed down the military rear sight dovetail to lower the rear end of the rail. Didn't dawn on me until after I had the gun blued. I may still do it. For now a shim cut from a plastic shotgun shell tube underneath the forward end of the rail is working fine. I guess I would be concerned about electrolysis using a raw aluminum shim against steel receiver and screws? I cut my shim full length and width so there is no gap between the rail and receiver ring. Marked the position for screw holes on the plastic shim and used a hot poker to open them up. Shim was cut from black plastic Peter's shotshell to camouflage it. You wouldn't know the rail was shimmed just looking at it.
 
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Actually, by shimming the rear base he should be bringing it more and more INTO alignment with the front base, hence REDUCING the stress on misaligned rings and scope tube.
Not if they’re lined up properly in the first place. If they are, then shimming would serve to raise the rear ring above the front.
 
The basics in a ring alignment and lapping kit

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