Will steering stabilizer correct highway "floating"?

No, your 33x12.50 tires are definitely (!) not supposed to be at 35 psi. If you read that 35 psi on the sidewall, realize that's not what the tires are supposed to be inflated to. The psi molded onto an automotive tire's sidewall is only the tire's maximum allowable safe air pressure which would only ever be used if the tire was forced to carry its maximum possible load. Since vehicle tires are designed to be run at about 50% of their max safe load, to give a safety margin, you would never inflate the tire to that pressure.

Not to mention the same exact tire might be mounted on 20 different vehicles that all weigh differently and the same air pressure would of course not be correct for all of them. The correct air pressure depends on the vehicle weight. So for automotive tires, the tire pressure on the sidewall is never correct. Where the psi amount on the sidewall is correct to use is on other types of tires like trailer tires and bicycle tires.

26 psi is definitely appropriate for 33x12.50 tires for a lightly loaded Jeep, go no higher than 28 psi when it's fully loaded with people and/or gear. The bigger the tire, the less air pressure it requires. Which is why my Bianchi road bike's skinny racing tires were inflated to 115 psi to carry just me and the bike. For my 35x12.50 tires, my street pressure is 24/26 psi.
 
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No, your 33x12.50 tires are definitely (!) not supposed to be at 35 psi. If you read that 35 psi on the sidewall, realize that's not what the tires are supposed to be inflated to. The psi molded onto an automotive tire's sidewall is only the tire's maximum allowable safe air pressure which would only ever be used if the tire was forced to carry its maximum possible load. Since vehicle tires are designed to be run at about 50% of their max safe load, to give a safety margin, you would never inflate the tire to that pressure.

Not to mention the same exact tire might be mounted on 20 different vehicles that all weigh differently and the same air pressure would of course not be correct for all of them. The correct air pressure depends on the vehicle weight. So for automotive tires, the tire pressure on the sidewall is never correct. Where the psi amount on the sidewall is correct to use is on other types of tires like trailer tires and bicycle tires.

26 psi is definitely appropriate for 33x12.50 tires for a lightly loaded Jeep, go no higher than 28 psi when it's fully loaded with people and/or gear. The bigger the tire, the less air pressure it requires. Which is why my Bianchi road bike's skinny racing tires were inflated to 115 psi to carry just me and the bike. For my 35x12.50 tires, my street pressure is 24/26 psi.
Thank You Jerry, you've been very informative and I greatly appreciate it!
 
Get it aligned, or diy, and get the tire pressure to 26-28 psi and report back. Without doing either of those you are wasting money and causing unnecessary frustration.

The camber is fixed on the TJs (no independent adjustment) but the proper pinion sets the caster within acceptable limits.
 
Get it aligned, or diy, and get the tire pressure to 26-28 psi and report back. Without doing either of those you are wasting money and causing unnecessary frustration.
Making arrangements today, to do just that! Thank you so much for the experienced adviced, very much appreciated. Hope to report back with good news tomorrow, you guys have been great!
 
Now I'm getting a little addgrevated. That "float" issue is still there. The wheel doesn't pull to any one side in particular, it just floats from side to side, so it feels like you're always trying to anticipate and fight the wheel on the straight aways.
1) Tire pressure — check
2) Tie rods and ball joints inspected - check
3) Steering box adjustment - check
4) New gas filled shocks - check
5) New steering stabilizer - check
6) New upper & lower control arms front & back - check
7) Sanity... no check
I'm puzzled, as there is not anything visibly wrong. A friend of mine has the exact same jeep, same year same lift, same size tires, etc... and does not have this problem. We were comparing everything under my Jeep, to everything under his, side by side yesterday. There were no differences except all my parts were new! I have not changed the track bars yet, but really don't want to keep changing parts, just to have no change in the results!

Mine was doing it and I had a bad unit bearing. Replaced it and it went away
 
I would have expected to see front end alignment (toe-in) checked. The steering system design on Jeeps means it won't "pull" to one side if mis-aligned, but not enough toe-in will cause the front to feel loose. Additionally, when you say upper/lower control arms, what do you mean? Are you just looking for play in them? If so, check your front pinion angle in respect to the front driveshaft. When I put adjustable ones on and dialed them in for the pinion angle, along with a re-alignment, my steering improved 100% - no float. The camber is fixed on the TJs (no independent adjustment) but the proper pinion sets the camber within acceptable limits.
I changed the upper and lower control arms in bothe front and rear, buecuse all the bushings were worn and dry-rotting. The Jeep goes into a local shop tomorrow, that services lifted vehicals, for a full alignment, and review of everything that I have done so far. I will adjust the tire pressure tonight, if needed, and see how everything goes from there!
 
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I changed the upper and lower control arms in bothe front and rear, buecuse all the bushings were worn and dry-rotting. The Jeep goes into a local shop tomorrow, that services lifted vehicals, for a full alignment, and review of everything that I have done so far. I will adjust the tire pressure tonight, if needed, and see how everything goes from there!

I have a 3.25" lift and 33" tires so our Jeeps are pretty similar in lift. I ended up putting adjustable lower control arms on mine (probably could have just gotten cam bolts and adjusted them that way - 2000's didn't have cam bolts anymore). I would suspect you can get some pretty favorable results if they dial in the camber (via pinion angle) and do the alignment. Let us know how it turns out!!
 
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I have a 3.25" lift and 33" tires so our Jeeps are pretty similar in lift. I ended up putting adjustable lower control arms on mine (probably could have just gotten cam bolts and adjusted them that way - 2000's didn't have cam bolts anymore). I would suspect you can get some pretty favorable results if they dial in the camber (via pinion angle) and do the alignment. Let us know how it turns out!!
Thank you!
 
Let us know how it worked out man and what was causing it so we can all learn.
 
If the hub bearings are worn, it will wander and follow lines in the road.
 
Let us know how it worked out man and what was causing it so we can all learn.
I will let you know how it drives when I get iy back, I finally brought it to a garage that has experience in lifted vehicals. The parts should be in tomorrow. I drove about 20 miles on the highway to get it there, with the tires adjusted to 26psi whiched helped a little, but it still got pretty scary going down the highway. After the alighnment, the owner called me up and said I had a few other issues dramatically effecting my steering.The passenger side caliper was hanging up so bad, that you couldn't spin the wheel while it was up on the lift.Secondly, my steering box has been binding for quite some time, and binding the steering column. So... two new front calipers, new gear box, and new steering coupling on their way in! Progress to be determined!