I was hoping that someone more knowledgeable than me would reply by now, but FWIW...
I don't know if this is the right way to be doing the math on this sort of thing, but if you take the aforementioned 5.7L/3.73:1 truck's 7500 lb capacity, divide it by the 3.73 gear ratio, and then multiply by your 3.42 ratio, you get 6876.
OR, if you take that website's 6000 lb rating for the 5.0L & 3.42:1 version, you could take the 6000 lb capacity, divide it by 5.0 liters, then multiply by your 5.7 liters, and get 6840.
TBH, I'm not real confident that this is the right way to calculate tow capacity, but I feel like it's gotta be somewhere in the neighborhood. I'm sure there's a much more nuanced and accurate way to do it, but 6840 and 6876 are pretty close to one another. I think you'll be fine pulling that trailer with a weight distribution hitch, just don't add too much weight to it.