One of the contributors and site sponsors here has written a pretty interesting article WRT long range shooting with a .223 that was posted on the 6mmBR.com site, in which he explains his experiences shooting out at a mile with his .223.
Worth a look. That is Jerry Teo, from Mystic Precision.
To requote an old old expression, it's about the Indian, not the arrow. At 600 yards, you get to learn to deal with wind, Coriolis effect, elevation adjustments, air density and a bunch off other fun things, all collectively and unassumingly referred to as "conditions", no matter the caliber, if you expect to have good and consistent results. Bigger guns and heavier bullets trade one set of problems off against another.
Another consideration (more "conditions"!) is whether your loads will keep the bullet moving at supersonic speeds at the required distance. Going through the transonic speed range is...turbulent...and sucks up a bunch of energy. Not helpful for accuracy.
Have you tried heavier bullets than 55grain? Or are you just going by what you read? Guys have reported their 12 twist barrel stabilizing heavier bullets than that , but it seems to be that individual barrels vary in that.
Have fun!
Cheers
Trev