B14, welcome to the board!
68g bergers are a great coyote bullet!
Try going up on your powder charge some, .5g for three shots.
If the 68's fall apart, then try a 80g Sierra Blitz Boat tail with 40-41.5g of IMR 4064 with a fed 210 primer with Winchester or Lapua brass, this load works in many 243's, start off at 39.5g and shoot three shot groups increasing your load .5g at a time. Best accuracy will be right at a max load for the rifle more than likely. Varget did not work with this load like IMR 4064 did, and the velocity is very good, accuracy even better.
