I think Blue Dot is gonna really suck in .357 Magnum with those bullets because you're going to have to load it down to keep the velocity below 1200 or so. Blue Dot likes to be loaded hot -- but not too hot. A faster powder, like Unique, 231, Bullseye, or Red Dot would do you better.
Since you have so much BD already, might as well try it.
Maybe it will burn right before you overdrive the bullets and the accuracy falls apart.