The rifle is a duffer (it happens) , the load needs a change or two or its the shooter well off par that day ?. Your not using the same old powder you had for another firearm are you ?Yes, you can get bullets to stabilise. The issue is, said bullets aren't exactly effective and are certainly not effective past a couple of hundred yards because they've got the BC of a brick. Usually the minimum velocity for lead free expansion is around the 2200fps mark and said bullets will drop off below that before 250 or so (barrel length dependent).
Im trying load development currently for a 1:8 tikka. Ive got the benefit of a fast twist barrel but im really struggling to get anything under inch and a half. My usual lead load will literally put a bullet through a bullet hole (pretty sure I've actually got a video of it somewhere).
Not all rifles are equal. The majority of lead free bullets aren't the right choice for much over 200, especially in 6mm.
I have had zero issues on the .260 rem 1-7.5 twist with any lead and nil with any of the 100 grain and 120 grain copper from Barnes tTSX ( 100 grain works the best on expansion at 300 plus yards ) Normally it will exit far side but some angles means not always . I VERY MUCH RECOMEND Barnes tTSX
Only issues i have had with copper expansion is with my 223 on CWD Barnes and Hornaday 50 grain and have therefore gone back to lead Nosler 60 grain