I think the options you have are the best of both worlds - shortening the 7x57 might make it useless with harmonics changes and lack of speed with the shortened barrel but you still have a handy .308 short rifle when needed.
If anything suppress the 7x57 so it takes the same can as the .308...
I find this with my hunting .308 - took it from 24" to 20" (didn't go shorter as I had an inkling I'd regret it). I am regretting going that short with it, as I'm finding that it just isn't generating the speed that the comparable but heavier barreled 20" version I have. The one I shortened is a 1-10", the heavy barrel is a 1-12" twist so you'd expect maybe a bit of difference but the 1-10" appears several hundred fps slower. Scratching head as to what to do now...
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