Ditto the comments on the Ford 6.0L...do a lot of research on that engine before you take a plunge. A high mileage, 9 year old 6.0L could get expensive real quick. Just one example: frequent-poster here 'skipnchar' towed a bunch with a F-150 5.4L, then bought a used 2004 F-250 6.0L and after lots of shop time and $$$$ now drives a F-150 Ecoboost. I mention him because you can find good info here by searching and he's a knowledgeable helpful guy. There's tons of examples like that. I know a lady who blew the head gasket on a never-tuned, 6 year old Ford 6.0L at 50K miles.
With the loads you are talking a gasser would have no trouble. Diesel vs. gas opens lots of discussions (check the sticky at the top of this forum if you have a few hours), but if your annual mileage is low-ish the gasser economics are hard to beat. I ran the numbers for my situation when I bought new in 2005 and ended up with gas (see sig).
As to your Nash, I've pulled my Nash 22H (about 6K loaded) hundreds of miles around the Rockies with my V10 and my Toyota 5.7L and can say the Toyota motor does just as fine a job. I can run any grade on I-70 west of Denver at the speed limit with it, under 4000RPM, except when it gets above 10,500ft, where I need 5,000 RPM. That's about 2 miles on I-70.
So like others have said, you may be fine with a larger-engine'd 1/2-ton class. The Ford F-150 with the heavy duty payload package #627 gets you a GVWR of 8200, giving you most of a F-250 in payload without the fuel penalty of the larger chassis. Look around and you can find those used as well (pre 2011 had the 5.4L and a 4.10 10.25" rear end), but they are rare so you might have to search a bit. Only Ford offers a 1/2-ton up-payload option that's not a rebadge'd 3/4-ton (both the Chevy 1500HD and Ram 1500Mega of years past were just 3/4-tons in 1/2-ton clothing).
I went through the 1/2ton SUV buying choices last fall when I bought my Sequoia for a family hauler, TT tow vehicle & Colorado byway adventure rig. I tow a Nash 22H (5K empty) with an Equalizer hitch. I need to get on a scale with it loaded, but I suspect it's about 6K loaded. The interior, powertrain, and four wheel drive capability tipped our decision to the Toyota. The payload is indeed a drawback, and we chose to favor the first three and buy a smaller TT to deal with the payload. I searched a lot of threads on here, and was helped by some great posts by a number of Sequoia owners, including "Drbolasky" who has weighed in here as well.
I've towed my Nash 22H (5K empty) with both my 2011 Sequoia (5.7L, 122" wheelbase) and my 2005 F-350 (V10, 173" wheelbase). The Sequoia with the Equalizer is more stable and gets better mileage by 1-2 and delivers better performance. For anyone familiar with I-70 west of Denver, my combo can make the speed limit on any grade there. Due to the gearing and lower curb weight, the Sequoia can outclimb my 3V V10 and is much quieter doing it. Of course, that's not all the story but just one data point.