I just went through this similar situation, that steering stabilizer (or any) shouldn't/wouldn't cause true death wobble. That in conjunction with loose bolts in the track bar, worn ball joints and / or tie rod ends, loose control arm bolts will definitely cause or contribute to death wobble. I agree with WJCO, start with the track bar connections, and steering linkage first. There are some really good articles that will take you step by step on how to test and check. Invest in a good torque wrench and check the torque on the track bar and control arm bolts. They should be 125 foot pounds if I'm not mistaken.
Mine turned out to be a lot of things causing death wobble, and all of them combined were the ultimate issue. New ball joints, tie rods, grade 8 bolt swap, torquing EVERYTHING properly and a new upgraded steering stabilizer fixed my issues. I ran the steering stabilizer off for a week after all repairs just to be sure it was right. Take that stabilizer off and you'll quickly find you've got some bigger issues. DW is dangerous and can be very aggravating to nail down so good luck!