22 feet of trailer and 3.5 feet in front.. my bad for misquoting.

 

Actually, that is a fairly light load. Curious, how did you arrive at the existing cooler is not adequate and transmission is overheating? What tool was used to determine that? What temperatures are being seen.
With that trailer and load, imho you do not need to do anything. The 1500 will not even break a sweat with that setup. Good to go. Just turn the key and drive. Just ensure to push the tow/haul button when running the rig to avoid damaging the torque convertor lockup plates. And most of all drive it like a truck that is towing a load, not a car rip-roaring around town or the freeway. Apply power smoothly 1/2 to 3/4 throttle, never full, and keep highway speeds in check.

 

I had the exact same setup with my 04 1500, you shouldn't be having any problem at all. I think your trailer probably weighs closer to 2k lbs, but still not a problem. Did you truck ship with the towing package? The towing package included a trans cooler, but it was pretty small. However I never had to upgrade mine at all, and had that truck from 4 miles to about 145k miles. I still have the trailer that I used, and was bought in 2005.

You can put your vin in here and see your truck's original config here:

https://fcacommunity.force.com/RAM/s/equipment-listing

If you transmission overheated, I would change the fluid while you're increasing the cooling capacity. Don't want to toast your transmission, they are expensive to repair.

BTW, are you using "tow mode", there is a detent button on the shifter end.... you should be.