I realized that I misread your post OP, so I'll clarify a little bit.
I've owned a 2-door JK for 11 years and done a bit of towing with several small trailers. Keep in mind I have the "first-gen" 3.8 liter JK motor that is notorious for being gutless. The 3.6 Pentastar engines do better when it comes to power.
With 4:10 gears and an automatic my Jeep has an official tow limit of 2000 lbs. Pulling a 1900 lbs. camp trailer was downright unpleasant. Overdrive must be turned off because you won't reach 50 MPH with it on. It took all she had to go 65 MPH on flats in 3rd gear and going up a hill meant 45 MPH max in 2nd gear with RPM near redline. Going over a pass was a chore. Spooky, embarrassing, slow, and dangerous.
Then there is tongue weight. My JK has a 200 lbs. limit with pretty much limits you to a 1900 lbs. trailer (if you want to stick with best practices). A 3000 lbs. trailer is going to put you at ~300 lbs. on the tongue...which is going to really pull the weight off of your front tires due to the short wheel base. Steering on winter roads will be seriously dangerous.
I wouldn't try to tow 2200 lbs, much less 2900 lbs. in a 2-door JK during spring, summer, or fall. In winter I would not tow at all.
A JL might have slightly different specs, but I'll be the HP and wheelbase is nearly identical to a JK. You will of course run into several people that say, "I have a 2-door and I tow 6000 lbs. boats all the time, blah, blah, blah.". They are either lying or stupid. And dangerous.
Will a 2-door Jeep pull a ton+? Yup.
Will you want to do it more than once? Nope.
Buy a 4-door JL man. Problem solved! Higher tow rating and longer wheelbase. There are also a lot more options for you out there for "Overlanding" goodies if you have a 4-door.