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I'd recommend the Adler lever-action with the synthetic stock and 20 inch barrel for handiness.
I am a big fan of the 7x57mm Mauser and applaud your choice of the Winchester Model 70.
It was put there only to reduce the strain on the firing pin spring.
The higher the sights above the barrel the farther this point is from the muzzle.
Is this problem something I can fix myself or do I need to take the rifle to a gunsmith?
I published data for that old wildcat in my first reloading manual in 1980 and since then have left it out.
Also, you don't polish chambers with a steel brush and metho. What blacksmith welded up the bolt face?
The T-Bolt's action is plenty strong enough to contain the .17 HMR cartridge.
I reckon it'd be a real barrel burner - even worse than your .223WSSM - but what a performer!
Mil-spec cartridges are normally loaded to pressures up to 15,000 psi higher than sporting .223 ammo.
That famous old bear and lion hunter you mention was Ben Lily who left his wife to chase a hawk that was killing his chickens.
Hitting 2100fps with a 17gn V-Max bullet the Mach 2 was a little brother to the .17 HMR.
If you can't place your bullets on paper, you aren't going to be much of a game shot either.