I'm not a member of the weight police either. Probably the furthest from it.
I've also towed countless trailers personally and professionally as well as had almost every model of F150/F250 from the early 90s to mid 2010s, including a handful of 4.6L tritons. Company trucks, new one very year basically, drive the piss out of it, work it, tow heavy sometimes, pass it down kind of thing.
I would tow 6-7klbs if I had to, with an old 4.6 truck, but generally under great protest. And that is assuming your truck is new enough and/or in good enough shape to basically run it at it's limits, power wise. If it's a high mile bomber (considering it's a minimum of 11 years old and possibly up to 25 years old) it's a hard NO.
If it's a good, tight, capable truck and you're not planning on running it through the mountains, the chassis and drivetrain will handle either of those trailers, set up right. Mountains = keep a spare 4 way flasher because you'll wear one out going up the hills.
With the 4.6, you have the lighter 8.8? rear axle and not awesome gears for a 4speed trans. Again solid and capable will pull it, but be very kind to the truck when towing.
