Major red flag - you’ll need a bolt face that’s .590-ish, and your action will need support for the ~1.6x bolt thrust you’ll get from the same pressure on the larger face (vs .474 for the 7x57).
The other issue you’ll see is that you’ll be limited by the pretty short overall cartridge length of the 7x57 of a hair over 3 inches, if your magazine and feed ramp are limited. You might not be able to fit the 3.34 COAL of something like a 7-270 and still feed.
Given that, my recommendations are to do some combination of:
- Burn out your barrel with 7x57
- Rebarrel to a tighter twist
- Pay the gunsmith to alter the magazine (box?) and feed ramps for max COAL of ~3.4 inches, then go 7-270 or 7 Sherman (which in this case is basically 7-270 Ackley Improved)
- Chop the barrel forwards, re-thread, and go something like 7-08 loaded long