First off have your tires rebalanced. That is the major cause of shimmy. Second jack up the front end ( both tires at once)and shake each tire side to side by hand and check tie rod ends, pitman arm and idler arm ends for excessive play. The alignment shop should have already checked for this. If theres play, replace the faulty part. Replacing the steering stabilizer will have no effect on reducing the shimmy.

'04 Taco x-cab 3RZ FE stock (daily driver)
'90 x-cab 22RE stock
'82 Hilux 6" lift (ACES HI)
'82 2-Hiluxs' Rally Edition (parts)
'81 Hilux 3" lift (parts/restore)