Is it the same length action as the standard military mauser action?
It may be a 03/38 conversion.
Many Turk 8x57s were actually converted the 1903 "K" action that was originally chambered to 7.65x53.
They can be identified by the semicircular notch machined in the receiver ring so stripper clips could still be used with them.
I think the metalurgy in them is actually better than the later 8mm rifles, not that there's anything wrong with them, but the 1903 rifles were Mauser factory contracts and were meticulous.
A friend tells me of his grandfather who fought the Turks in the Middle East during WW1 and the Turks were gave up their rifles when they surrendered.
He passed a massive heap of said Mausers when leaving one town and he said any of them was 10 times the rifle his SMLE No1 Mk3 was in terms of fit, finish and function.
The British burnt the lot.
But I digress.
If your action is an 03/38 a "T'wede" or "T'illean" (Chilean 7x57 bbl) is far more suitable.
I have the 7mm bbl and 03/38 action stowed away for a T'illean when my oldest son starts to hunt deer.