I have a .243 on a old 98 Mauser action. Feeds quite well
Some years ago I bought an older custom rifle, probably built in the 1960s judging from the stock styling. It was a .243 with a 26" heavy barrel, built on an intermediate length Mexican Mauser action. In theory the shorter action should have fed .243s well--but did not. It took me half a day to get it to feed right.
Which is only one of many examples of how controlled-feed actions are harder to get to work correctly with certain cartridges than push-feed actions. But even PF actions can vary considerably with different rounds--which is why I suggested to the OP that trying a few 6.5 CMs would answer his question.