When you changed your steering stabilizer, did you loosen anything else?  Check the bolt torque on your steering stabilizer are at 50 ft-lbs.  Anything else you touched, make sure it’s right!
Looseness causes this issue and it sucks donkey balls!!!!
Next Check the following:
1.  Track bar bolt torque at 125 ft-lbs both ends and track bar bushings intact and not degraded.
2.  Tie rod ends have no play and bolts at 63 ft-lbs
3.  Drag link clamp bolts at 26 ft-lbs and end links with no play and at 63/77 ft-lbs
4.  Ball joints have < 0.060” vertical travel and very little side to side movement.  
5.  Caster at approx. -4 deg
May want to lay under the Jeep while someone slowly turns the wheels back and forth to identify any loose parts.  
My death wobble ended up being a loose track bar to axle connection along with a wallowed out hole in the bracket.  Installed a high steer bracket and drag link flip to solve it.  
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