I'm surprised you think the 338ME kicks like 45-70. I never shot a 45-70 but shot my 444s with 300 gr. JHC at max charge it's harsh after a few rounds. I shot 30 rounds sighting my 338MX and being a hard kicker never entered my mind.
I've shot up to 60 rounds bench shooting my 338MX. It's subjective but to me the 338MX is only slightly more recoil than my 308MX.