A few contributors have suggested that they very quickly would have applied the Airspeed Unreliable memory items. ( flight directors off, 10 degrees NU and 80% thrust on the NG) . I think that the confusion when presented with a lot of information in a short space of time in a dynamic situation is often underestimated. It takes time to process information, and then more time to conclude its meaning and decide on a course of action. Salience is often key and I suspect that the stick shaker had it in spades. If the stick shaker did initially consume much of the Captains cognitive capability, then reducing thrust may not have been seen as a wise choice so close to the ground, with an inability to lower the nose much just after rotate the next pertinent step is to increase thrust if the stick shaker is valid.Confusion already in the first second or two is possible/probable.
Edited to add: ATC WATCHER I posted the above simultaneously as you posted with pretty much the same sentiment but without having read your post.