Priest has been probably top 3 most annoying classes hunter/zoo/priest in that order. My record prior this recent winning streak against press was 8-22 this season in ranked, that is bad right?
My strategy against priest has always been try to get board control fast, get as much damage and dont let him draw cards. So i will clear cleric right away. I think this was the wrong strategy, after losing 7 in a row and dreading playing priest, i figured i'll just let him draw cards and hopefully if i get to the end of the game, he will fatigue. Well that worked and now i am on a winning streak against priest. IF you can get to the late game they will run out of options on giving damage. So my opponent in my games get to the point where they know they are running out of options and they are mind controlling minions like like harrison jones! lulz. Once they do that, then it is safe to drop tirion. I never drop tirion till the very end.
I've been reading many people having struggles with priest which i was one of them, but i think the strat of letting them fatigue and dragging out the games is the way to go.
I play a deck similar to koyuki's, so hopefully this strategy may help others struggling with priests.