Op only got one response on an Alpine FW, but sounded positive.
It appears in OPs sig, that he may have switched gears in his 04 350. One line says 3.73, and another 4.56. With the 4.56/V-10, he should be able to pull the 15K fully loaded trailer. I also think the RAWR of this vintage was 6,8XX, so should be able to carry the weight. Tires should match the RAWR, likely slightly more.
I do agree with Chris, as to a new truck in future, if buying this trailer.
Any of the newer 35 series diesels would work much better for extended trips.
Jerry