Later is best. I would come in late August or early Sept. I live here, not because of my job, but for hunting/fishing. I don't even look at my flyrod until July due to water conditions. The Yellowstone is still high and off color and most streams are still that way.
I will be fishing next week, the week after for sure. The waters will be clearing by then. August is good for lots of dry flies, hoppers are common by then, but early Sept-October is still best.
If it is only May or July for you, I would certainly pick July...