I favor the wide grip/narrow stance setup for most tires as well. Get the shoulders into the tire if it's tall enough, get the feet about squat stance, and drop the hips to below shoulder height. I've been taught to get more of a forward drive into the tire, vs a deadlift/knee/push over setup. As the tire is passing through around 45 deg, you'll be able to initiate a big knee and hip extension, and from there drop under quickly and walk through.
keep your hands on the tire as the flip is completing to minimize wobble, and to make sure you're getting right back on it for the next flip.
All of that goes out the window was a tire outside of your normal flipping ability, like Dave said.