That's not Death Wobble, you absolutely cannot accelerate up past true DW to stop it. That's simply a speed sensitive shimmy which is night and day different from DW. DW is so violent beyond the ability to comprehend until you have experienced it that it's hard to describe. The only way to stop DW is to immediately slow down to nearly stopped.
Get your tires balanced, that should take care it. And the correct term for a steering stabilizer is a steering damper, its job is to isolate the steering system from shock and jolts. A new one is NEVER EVER the cure for a shimmy or DW. It might temporarily suppress the symptoms fooling some into thinking it cured the problem but it's only temporarily suppressing the problem. Like holding a gorilla down, you're eventually going to get tired and the gorilla's gonna get back up and have his way with you.