I have only owned one 8x57..."supposedly" it was a battlefield pick up in Russia, which they, in turn cleaned it up and sold them. Mine was a K98 and it had Nazi markings. I had a taller front sight put on and I only shot Turkish surplus ammo. Some said it was machinegun ammo, I don't know but it was hot stuff! My point is that it was ( still is, I gave it to a young man in my church) a great shooter! I won't say how good as I don't want to be thought of as a liar...but it was/is, with that ammo, at "least" a 1 MOA rifle.
I say that as I believe any 8x57 is worthy of tricking out, investigating, trial and error, doing everything one can to get them to shoot acceptably. To "me", I'd want at least a 2 inch/100yd setup. I can't accept bigger than that "for myself". I have "put in my time" with a rifle like that ( my dad's old Mod 742) when I was a young man. We shot it iron sights and it would do about 5-6 inches with 150gr Corlokt ammo. It didn't much matter as I never killed game over 50-60 yds with the thing! ha I later got some of the new Federal "Red Box" factory loads that used the Sierra 165 SBT. It then shot a nice, rounded 4" group. Still didn't matter, I hunted int the heavy woods with it, everything I shot with that particular load was under 40 yds! ha. So, I'm glad some guys are still messing with the older Mausers, but they can be shooters. It is certainly a powerful round. A friend of mine shot his cow elk with his old Persian Carbine 8x57 and 200 Nosler. His little rifle is a real shooter too.
For a safety Shaman, I think you could find a Mod 70 type pretty reasonable. someone put a Wisner Mod 70 type on my 7x57 Classic. It needed a bit of work to smooth it out, but it is fine now. I never had an issue with the Remington thumb safety, I really like them in fact. Good luck to you Pard.