Death wobble simplified
All front ends can and will death wobble for one reason, and one reason only. The front end as a unit is unable to control the oscillating force of the rotating tires.
Once that is understood, you can start to evaluate individual cases like yours.
From the picture it looks like your jeep is equipped with 35” tires and possibly steel rims, that likely have a shallower back spacing.
One thing you need to understand is that your jeep was designed to handle a 32 inch tire on an aluminum rim with almost 5 inches of back spacing. As you increase diameter, weight, and leverage, you can push the front end past the point where it is able to control the tires.
As the individual front end components wear, it becomes more and more difficult to control the tires.
You can have death wobble on a stock jeep that has an excessively worn front end. You can have death wobble on a brand new jeep that someone slaps a lift and 37’s on.
From your description it sounds like you have to much tire and rim for your front end to handle reliably.
You can and should run balanced tires and maintain a good condition steering stabilizer, but, those things really only help extend part life. If your front end is compromised enough, you will experience death wobble regardless of tire balance, or steering stabilizer condition or presence.
That is the problem with budget suspension systems. They supply just enough parts to get you into trouble. You have two choices if you want to make your jeep considerably more reliable in the terms of controlling death wobble.
1. you tone down the wheel and tire combo so that the front end can better handle the forces applied. Which you can do by using deeper back spacing aluminum rims, smaller diameter tires, or a combonation of all of the above. Heavy sidewalls such as d and e rated tires also help.
2. You can further upgrade your front end to better handle the addition of the 35 inch tire and wheel combo. While expensive, its cheaper than new tires and rims, and is an upgrade while spending money.
Get your tires balanced for now, but realize that you will just be prolonging the onset of more death wobble and potentially damaged parts if you don’t address the major issue of controlling those tires sooner than later.