There are photos of 24's in the new member's section. To fit properly they have to go down to a 35 aspect ratio. You would be at what, 40? There is very little sidewall. And I would think that tire pressure would have to be very high at the rated load capacity, even if you could find 22's with enough load rating to tow.
Now, some common sense advice which you may either take or leave: Not to burst anyone's balloon either, but towing 5,000 or even 6,500 lbs. is not the same as 8,000 lbs. With that load on my Armada, the rear bumper just starts to sag. Not much, but maybe an inch. That means that the air bags have fully lifted as much as they can and that the suspension is very, very stiff.
Don't get me wrong, your truck will tow the 8,000 lb. load quite easily regardless of the tires and wheels. You have the engine and tranny to pull it down the road almost effortlessly. If you are experienced in towing trailers in this weight range, I apologize in advance, but am only trying to help. To tow safely, you gotta have the right tires and some other equipment. Be sure to have very good progressive electric trailer brakes with a good controller and a weight distribution hitch. 8,000 lbs. is getting into 3/4 ton truck territory.
And, if I may suggest so, please read the "sticky" thread on towing. If you have not previously towed with your truck, also please, please, do the proper break in procedure for the rear differential or it will turn to toast. You gotta let it go through controlled heat up, cool down cycles to heat treat the gears at full contact mesh. They are not at full mesh when you are running with no load or a light trailer. Once that is done, though, you should not have to worry about the differential. I think we covered that process in the "sticky" thread. Do watch your transmission temperature gauge and DO NOT TOW IN FIFTH GEAR. Set in in fourth and leave it there when a trailer is out back.
Are you going to be doing any of your towing at altitude or climbing or descending hills? That would also be a factor and will effect weight transfer to other axles when you are running flat and level, and will also effect braking.
Many people suggest that when the trailer weighs over 20% or more than the truck, you should probably not exceed 60 mph, even though you can run much faster, because if something happens out there on the highway you get into a tail wagging the dog situation and things can get really, really ugly if you have to make an emergency maneuver or have a flat tire or things like that. I don't know if that is true, because I limit towing that trailer with that load to 60 mph, and that is on level ground.
Maybe I'm just too conservative. I am 55 years old and have been towing loads this heavy or heavier for quite a while. My "other truck" is a 7.3 Ford F-250 Super Duty diesel. It usually tows that trailer, (and some heavier ones) but sometimes I need the 'Mada to move that one.
Have fun. Enjoy your new truck and your new "toy" hauler. Play safe.