While I haven't tried the 77 gr MK in a slow twist barrel, I did try the 107 gr 6mm bullet in my 1:10 .243, they didn't work.
Bryan Litz suggests the 77 gr MK in a 1:9 barrel has a nominal stability factor of 1.39, where 1.4 indicates marginal stability; meaning that at sea level with 50% humidity at 59 degrees F, and 2800 fps muzzle velocity. Higher than 1000' of elevation, greater humidity, warmer air, and higher velocity all work in your favor, where for me at sea level with 30% humidity at -30 and 2600 fps velocity in the same barrel they won't work.