If the vehicle is in good condition and well maintained just take your time. Your not going to win any races, nor should you want to. A more robust TV would be great, but if you are safe I'd go camping. Not everyone can afford a new vehicle.
That said, I do think 7k is optimistic for a tow rating for a Aviator (basically a explorer). I pulled the same trailer manor 3023 with both a 99 Ford Ranger with the 4.0 V6 and then with a 98 Explorer with the 5.0 V8. With the 5 speed trans and 4:10 gearing the Ranger was a much better experience. Lots of things go into a good TV imo.
FWIW. That same trailer I pulled with the Ranger, I then put behind a 1 ton diesel. Guess what... they both did the job, held acceptable highway speeds and got us there.