Wow, a lot of responses regarding my plans and I’m glad for it because like I mentioned, I’m not an expert.
Thanks to jeffd for posting up the capacity published in the owners manual. I down loaded it and found the following:
Sport S with Max Tow has a combined GVWR of 12,800lbs. Subtract the Gladiator GVWR of 6,250 and that leaves 6,550 for towing if the truck is loaded to the maximum weight. It’s misleading that Jeep advertises 7,650lbs, but it would be possible under the right circumstances (ie nothing else in the truck).
Unfortunately both the 27’ and 25’ trailers would be too close to or maybe even over the combined GVWR when loaded. If we decide to go this route then a bigger truck is the prudent thing to do although less fun!
At this point I’m still considering the 23’ and more specifically the Globetrotter 23FB Twin. This trailer has a dry weight of 5,300 (with 60lbs propane and batteries, no water) and a max weight (GVWR) of 6,300. Obviously, the black and gray tanks would be empty or mostly empty while traveling, but I would have some fresh water on board up to a couple hundred pounds to possibly the maximum of 39 gallons or 325lbs albeit unlikely.
Again, thanks for all the responses as they have given me even more to consider!