Think I've answered my question - with thanks to the inquiring prodding. Interestingly it doesn't involve gas or diesel. But please check my math!
Heaviest trailer: 13400 so 20% pin weight of 2680.
Add 4 adults @150 = 600
35 gallons of fuel = 250 ish (oil and other fluids)
Trailer saver TS3 hitch = 250
GRAND TOTAL 3,780
No 3/4 ton truck I'm familiar with will do that. Not even a newly discovered 2017 Ford f250 diesel.
With that thought I'm doing further research on 1-ton diesels. Either that or we give up until we get the lighter weight trailer.
Thanks for the help folks.