It turns out that the Stainless M77MKIIs had a different rifling twist than the other Ruger's in 350 rem mag. SO... I decided to try some 275 grain bullets.
I could not find any loading data for this weight so I played around until something worked.
These were the very old BARNES 275s made from lead. I only have a few left so each experiment was only 3 rounds. This load of 56.5 grains of Reloader 15 seems to work... I just bought some Kodiak bonded 358 caliber 275 grain bullets as well. They look almost the same. The Kodiak's are a touch larger in diameter around the base, so I may have to back-down the powder to find the sweet spot.
A 3589 caliber, 275 grain bullet (the Barnes' really weighed 276.3 grains) at 2,450 should work well