Whether you buy his claims or not, the key sentence in the Brandt article is:
"Unloading the saddle (without standing up) will stop shimmy."
Shimmy (to this non-physicist) is related to center of gravity. As Brandt suggests, it can start with hands off the bars, butt firmly on the seat (well, the seat on my bike is above the handlebars). So, to end shimmy, lower your center of gravity.
My first experience with spontaneous shimmy was several years ago on a 45 mph descent (oh, craaaaap!) and neither a death grip on the drops nor careful braking would stop it until I'd come almost to a halt. Headset adjustment didn't help either. What did help, on subsequent occasions, was to do just what Jobst recommends, although one could wish he'd been more emphatic: I did a little jump *down* onto the level pedals, and the shimmy stopped immediately! After a couple more successes and a little regained confidence, a friend suggested gripping the top frame bar between my knees, and along with unweighting the saddle (most of my weight on the pedals, some on the handlebar, none on the saddle), the dreaded shimmy has not reappeared, even with my hands at the stem. This is on a road bike, don't know how it would work with suspension. Hopefully induced shimmy would respond similarly.
Put your pedal to the mettle,
Crunchie