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Cant say I've experienced that much gain in velocity from a cold barrel or any appreciable difference in velocity from 1st to 3 shot when shooting groups.
Usually shoot 1 fouler if from a cold clean...

Nice shooting, that 1st shoot seems a fair bit faster than the rest, certainly worth loading a few more and checking consistency.

I had the seating stem in my 270win lee die machined by gunworks to match the eldx projectiles I use, works a charm ad was cheap as to about $20 from memory all they needed was my stem and a sample...