summitpower, My truck has a "tow rating" of 11,300... My truck will tow either of those trailers "by the numbers" too....
I'm towing a little 22', 5,000 TT with it and of course, it does it without any stress on me or the truck at all.
I towed it with a 97 F150 with a 5.4 in it for over 12 years and it did it well too... For what that truck was at the time..
I've towed trailers for the last 30+ years and have towed overloaded and have towed under the limits of the tow vehicle many times from coast to coast too.
Guess what my preference is now? :)
I would go up to around a 7500 GVWR trailer with my current truck if that time ever comes.. But, I'm not looking to change anytime soon. (notice I didn't include any DRY weight.. ;) )
If all you are going to do is take either of those trailers to your site and park it, you could probably do that with your current truck... It won't be the best combo by any means, but that's what maxing out ANY vehicle is going to be like.. Matching your trucks "tow rating" to a trailers "dry weight" is going to MAX out the vehicle.. No matter how you want to justify the numbers.. ;)
The only other thing I'd do is leave the family and anything else behind for the initial trip..
Drive back home, load up the family and whatever else you want and enjoy!
Shop for the new truck for future road trips.
Take what you learned on driving that empty trailer and empty truck no other passengers and stuff and use that to decide what your new truck needs to do for you loaded up with people and stuff. As well as the trailer being loaded up with stuff!
Good luck and we've all been where you are.. But, we usually only learned from the actual experience and adjusted from there, so you not having any experience yet.... What the dealer is telling you, is yes, by the numbers, your truck can tow this trailer... But, what he isn't telling you, is that once you load it up and the truck, you won't like it at all... ;)
Good luck!
Mitch