Yes, it is all about timing, no, there is no minimum speed, and A/E works find on the flats as well as in the bumps. A paper presented at an International Congress on Science and Skiing a few years ago documented how much quicker A/E turns were through the gates than the usual up-unweighting. A/E has been around a long, long time. See if you can find anything using the old term of down-unweighting.
You know how you flex your ankles/knees/hips to absorb the forces through a turn, then extend to transition to the new turn? Don't do it any more. Keep your legs, especially your outside leg near-straight through the turn and increase the edge angle to handle the increasing forces toward the bottom of the turn.* Shorten the inside leg as your lower body has more angle to the snow so most your weight is on the outer ski. When you're ready to end that turn and start the next, relax your legs and float across your skis to the other side. In a quick turn, you'll feel like you're pulling your knees up to your chin. You'll be in the backseat momentarily, but strongly pull both feet back as you let the legs extend to start the next turn.** Don't push the legs out, just let them extend. Hunt for every bump & lump you can find to practice on.
*Don't dig in the big toe of your outside foot, nor drive you knees into the hill, nor drop your hip toward the hill. Roll your inside ski on on it's outside edge and allow your lower body to move toward the hill while your upper body balances outward from the hill.
**Rule of thumb--if your ski tips are off the snow, you have no control. Get your ski tips back on the snow by pulling your feet back strongly.