Taking advice from The Big Book of Gun Gack (thanks JB) I used Hodgdon data for the 7-08, which has nearly identical case capacity as the 7x57.
With careful attention to the chronograph, I worked up to maximum velocity listed for the 7-08.
Ended up with 145 LRX at 2900 fps and 150 NBT at 2850 with excellent accuracy.
Winchester 70 22" of 2014 vintage - Hornady cases and 210 primers.
Since 7x57 throat dimensions, and therefore pressures, vary all over the place, please do not try this without benefit of a chronograph.
Cheers,
Walt