If I was stacking them higher, I'd think the "brick" method would be good, but with just two high, why make it complicated.....
I put tarps around my run to keep the snow from drifting in there, and then I also use hay to help keep them in place and also as a wind break as you mention.
Ohio weather gets very cold, windy, and the snow can get so darned deep! It's CRAZY! LOL I zip my run up pretty tight (it has a roof on it), and then I hang a heat lamp in there, suspended from the roof, a few feet above the water bucket. That helps keep the water from freezing so quickly.
I think you've got a great idea, plus if you've got the straw, hey that saves you money.