A new stabilizer is never (!) the cure for DW. It might help suppress the symptoms for a while but a steering stabiliizer is kind of like a skinny guy trying to hold a gorilla down. It may work for a while but eventually that gorilla is going to get up again when the skinny guy gets tired.
Imperfectly balanced tires are the most common root cause of DW, often in combination with the front trackbar not being rigidly held to the axle on the passenger side so it absolutely cannot move. The trackbar can move from the bolt not being tight enough or its mounting bolt hole being wallowed out from the bolt being loose for too long.
I would make sure the track bar is mounted TIGHT on its axle end, that have your tires perfectly
balanced. Tell the tire monkey that "good enough" for tire balance isn't going to be good enough, that they need to be balanced to 0-0 which is perfect.
If that doesn't do the trick, I'll be surprised but there are more things to try after this.
Also, I hope your front axle's toe-in adjustment is right on.