Try picking them earlier. Many people pick them before they even open up all the way, and say they think the center is unattractive. My wife and I pick them both ways -- when come of the colored outer bracts are still covering the center and when they've opened to the point where you can see the actual flowers. You're right that the flower heads themselves need practically no drying -- it's the stem that takes a while. Here again we disagree with many other people who dry strawflowers. We find the stems are plenty stiff and strong if they're well dried. Others discard the stems and use artificial ones.

Oh, the center of the Stawflower, the bright orange center, are my favorite part of the flower :). I will give both suggestions a try. Thanks Neil_allen, for the help.