Because you solved only part of your problem ..the loose components that can allow or exacerbate death wobble . Now you have to deal with those clapped out tires . The vehicle can withstand higher speeds , as it's tighter and fights back better , but the same root problem (the tires) is still there .
Death wobble can be only a low tire , out of balance tires , only loose components , but most of the time it's a combination of the last two. Not always , but usually. I know of one case where a brake rotor caused it on JK.
With 277,000 miles , you are way past needing some parts replaced up front , hence that unbelievably loose track bar ....and bad tires are not only shaking the vehicle , but accelerating wear.
The tire/chassis relationship is like the mind /body relationship..you really can't separate it , and there is no substitute for good tires. Some all terrains would be heavenly.
I will add this , and I would say this to my sister.....watch what you spend , you need a newer Jeep with less miles when you can swing it . At the same time , make it safe and if your heart is in keeping it , be thorough and we will support you with ideas all we can.
What happens on one with that mileage is parts get replaced as they fail , so you end up with parts of various ages , and they then fail at various times , which can seem like constantly.