The Cheytac parent case is more then capable of 1/4 moa. I use this case in my 338 and 375 AM and both have shot a load of 1/4 moa groups. This is my personal best three shot group at 1800 yards fired with one of my XHS repeaters in 375 Allen Magnum.
The three shot cluster measured just a hair under 4" ctc so well under 1/4 moa. The impact at the bottom of the gong was made from 4 hours earlier when I was trying to hit the gong in severe mirage and out of 5 shots, that's the only one that hit. Later in the evening, clouds came over, cooled off for no mirage and no wind, perfect shooting conditions and it showed with a great group as a result.
The Cheytac case is very capable of fine accuracy.
I would agree that I have a preference for lead core bullets for best accuracy over a wide range of different rifles. Solids can be very finicky depending on bore diameter but if the match is right, they can be amazing. Still, the lead core bullets ARE more forgiving over all.