Your 257's will do very well as well your 6's.I spoke to Seekins about doing a 20" 7PRC barrel. I've been told they'll do whatever barrel you want by them and been told differently. This rep said unless I order a custom shop rifle for $3900 then it's gotta be an off the shelf barrel option but said they could make me a 22" lightweight barrel like on the element so I could have a 22" barrel at least. I think that might be a better option weight and balance wise than going with an Element and I'd still have a 26" barrel to spin on if I wanted to use it to go shoot some ELR. If I was going to go the custom shop route then I'd just spend a little more and get a SLAM but that's not what I really want or what I want to spend.
I don't think this is the place for this debate but theres a huge thread on rokslide about it which you're probably aware of. It clearly works and there's people who live out in elk country that swear by it and people who travel to elk country who swear by it. It's not the tool for the job I'd choose but it's clearly effective and I wouldn't say it's not a right tool for the job. I've got a family friend that has gone out west almost every year since I was a kid and harvested elk, he brings two 6mm's (6-284 and 243 backup rifle) both shooting 95gr Bergers and has successfully killed elk every time and has shot some of them over 600 yards. He swears by it and I'd guess if he had animals getting away he would bring something else since he's got a pile of rifles.
On paper my 6ARC with 103ELDX doesn't dip below 1800fps until 600 yards and carries the 1600fps minimum expansion to 725 and based on shooting it at distance I would feel 100% confident putting one where it needed to go, but I wouldn't choose to use it unless it's all I had. I could even use it as my backup rifle and be confident especially since I could put 3 shots on target extremely fast, but I'd still like to hit a big animal a little harder and it's heavier than I really want to carry much. Any east coast hunting though it's 100% what I'm grabbing from varmints to white tail
What year and what state is your hunt at?
And not to turn this thread into the toidy but Mountain Sloths comments about "pumping 6mm slugs into elk" is way freaking off base and tells me a ton load about MS. I'd be for betting that as a general rule those using the vaious 6's put elk on the turf just as fast and with as few or less rounds expended than the big belted mags! Heck I know of more than a few elk who've made their way into the deep freezes on friends via 22/250's and Swifts.
Killing elk just isn't rocket science despite many people's efforts to make it so.
We all have our limitations, ideally people understand that and keep to those limitations....ideally