Looks like a lot of opinions here, now it's my turn
Even with the towing package, you still need to be within the weight ratings. That means trailer as well as the TV. While you may think that the trailer only weighs what the sticker on the side says, that is a dry weight - no water, propane, spare, food, clothes, "toys", utensils, tools and other camping clap trap that we all seem to accumulate. In some cases, especially the TV it's even unsprung weight which doesn't even include the road wheels!!! Of course, if you have kids, add their weight and the treasures they seem to be required to bring.
Now, that TV. My F350 say 6999 - yeah, sure. The truck weighs over 8000#. I have the optional 18" tires, a Cl 4 and a goose neck hitch with a 5th wheel adapter. I do have the gas engine, a V10 which weighs a bit less then the diesel. All of that gets me well beyond the 6999 pounds. This give you a picture of where you are starting as far as weight.
That 5.3 (327) gas engine - great over the road engine, but not a real torque monster so it will be struggling some up hills. Gas mileage - I would suspect that 10 would be a good day with 7-9 more likely pulling anything as long as a 30 footer. Another point that many forget - the front aerodynamics on most RV's. They are in line with the frontal area of a barn door, which conspires to kill gas mileage.
As far as towing - a longer trailer will probably need a heavier set of lift bars (550 vs 750 or more) and might even need a friction anti-sway device or two. I needed one when I towed my 30 footer with an F150. The F350 - didn't need it as the tires as well as suspension were much better suited. The current 34 foot - 5er - no problems.
What would I do if offered these trailer options you said you had - if at all possible, hook the 30' up and go for a 15-20 mile drive. The 24' wont cause any problems unless it has slides, then possibly..........