7X57? Sure, but what's wrong with 6mm Remington? Just run it thru the 257Bob die and BINGO, you've got it! I magine there are far more choices for 6mm Remington than 7X57 brass.
There is a difference in Headspace for the 6mm Rem. It is shorter than the 257 or 7x57. Manson uses the 7x57 go gauge for their 257 Roberts reamer. I have 6mm Remington AI brass that was used in my last failure for a long range varmint gun. I tried using the 1-8 twist barrel,,, total flop!
The flop was in pushing max velocity, anything over 3100 to 3150 fps and groups opened up the faster you pushed them, all the way to 3450 fps. lighter bullets were the same. Yes I could group 1/2" but thats over 4" at 800 yards If I did everything right, this means if I'm perfect,,, which I am not, especially in the field I would misses imposible to make up for.
At 3050 to 3100 fps the 108 and 105's were capable of 1/4" even now and then .2" 5 shot groups, 2" moa and less at 800, only way to miss is human error then. Plus even at 3200 fps, the bullets would slow down to much at that range to open up or do anything but poke a hole thru ground hogs and larger, which means more crawl offs.
Lighter bullets were even harder to drive max speed and get the accuracy needed for over 800 yard use efficiently. For this reason I'll leave the 8 twist barrels for what they are intended for,,, punching paper, not varmints at long range!
Now to that brass. I'm building a proven 800 yard plus varmint rig, and that needs a 1-10 barrel. In my opinion PERFECT, in 6mm or 25 caliber for this particular purpose! Mine is a 257, Roberts Improved. I chose the Bob from past experience, and even though there are faster 1/4 bores,, they EAT BARRELS! my experience has shown the Bob is about as efficient as it gets, and even the 25/06 gives far less rounds in barrel life, and requires more powder to do the same job, but is much harder on barrels when used to get the same results. The bigger cases just make this even worse.
I tried the simple fl size thru my forrester die, and found about .013" less headspace was the results using previous fired 6mm AI brass. Best results were just using my K&M carbide neck mandrell I use to turn my necks, needed for the 257 Bob cases I'm forming out of 30/06 Lapua brass for Bob getting into body thickness of this brass at the new neck location mean turning my necks even for my No Turn Manson reamer.
I then tried some 7x57 AI brass I had fired in a previous build, It showed .002" to .004" shoulder set back. Probably why Manson uses the 7x57 go gauge with their .257 AI reamer.
I think most will find using different reamers from different manufacturers, there could be a slight difference in the reamers. But make no mistake, Ackley Improved chambers for the 7x57 or my preferred case the Lapua 8x57, will see that the 257 and 7x57 AI's are a bit longer on drawings than the 6mm AI.
This is all part of the fun building these calibers, but make no mistake, you have to be well aware of the dimensions of your individual chamber to do this successfully as well as safety! They are a Wildcatted chambering and should be treated as such. I have never been able to find a SAAMI spec drawing for these cartridges, and does not specify the exact headspace for them.
Good Luck, and I have had great luck with the 6mm Rem. AI, but my best ever for varmint past 800 yards, and loads that allow a bullet to open up at that range, never poked one past that here in the east, is the 257 Roberts AI!