Keep in mind, extra steering dampers are just band aids for the real problem. You really need to give the car a good shake down to find the real culprit. If nothing avails from that, check your alignment, speaking from experience (lifted jeep 34" tires), if your tow is out, it will take you for ride, lol. I usually set mine a tick towed in from zero, yes it does travel and wander a tick, but no deathwobble. You'll have to play with that a bit, (say 1/8 in- testdrive, zero- testdrive, and 1/8 out- testdrive, for example), to find out where your car handles and reponds the best without wobble. Once your front end is tight and correct, that little shimmy shock won't help or hinder you until a component starts to wear out, if I chose to, I could remove mine from my jeep without any ill issues, I just keep it on for a just in case tie rod failure.
*Another thing that is commonly overlooked, tires, when's the last time you had them balanced? They can and will cause nasty vibes and wobble if they're out. I've been guilty of this one, lol, couldn't find the wobble after alignment, deceided to rotate my tires, wobble gone, next day balanced the two I swapped around, put them back to the front, no wobble, lol.