I had a 2010 JKU with the tow package. I used a SuperChips and added airbags to the rear to help stabilize a JayCo single axle camper. It weighed "wet" at about 3500#.
Towing it was a disaster. I had a WD hitch. I was an RV trailer transporter for the manufacturer for about 18 months with just under 200K travel trailer tow miles experience.
The 3.8 in no way allowed me to make any speed nearing normal interstate speeds. going up something as easy as an overpass would drop my speed to less than 45 mph and I doubt if I averaged even 5 mpg between northern Illinois and the Florida panhandle and back.
I promptly returned home and traded the JKU for an F150. I still miss that Jeep for the fun we had but it was not and never could bea tow vehicle for anything even remotely heavy.
I tow a similar Jayco with a much better result.
I'm on 33s with 5.38 gears. I set the tuner on tow mode. I have a wdh but no airbags.
I can maintain 65 on rolling hills. Real grades slow me down, but around here we have truck lanes. I go as fast as I can keeping the throttle about 50% as indicated on the scan gauge. I get 9-10 mpg.
I haven't weighed the trailer but I'm sure it's 3500#.
My trailer is a Jayco 165 sport. I lifted it 6" to keep the plumbing from dragging on gravel roads. The lift made no noticeable difference.
I read an engineering Q&A from when the JK was introduced. They mentioned the tow rating was based on engine cooling. I have to agree. If I run grades at over 50% then it starts to warm up even with water wetter. I'm thinking about a hood vent.
That said I think your LS will pull 4500 pounds just fine. Be prepared for all the warnings about death in a giant fireball only to be extinguished by your insurance company urinating on the wreckage because you exceeded 3500#.
By way of qualifying my comments, my last tow rig was an F-350 with a capacity of 19600#, and my trailer was a 40' gooser at 15k with 2 cars in it. I know what stable towing is. I've had several trailers in between 3500 and 15k over the years.
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