We tow a very similarly sized trailer w/ a very similar truck with no sway or other issues. Not an issue of not enough truck. I'm not sure, but maybe the E2 hitch doesn't provide sway control? We have the 4-way Equalizer, and really have never had any sway or trailer control issues. At any rate, you just need to get it dialed in.
There is a performance tune for the F150 ... it's called the 3.5 Ecoboost! Seriously, the 5.0 is gonna have to rev to make enough power. No problem doing that, but you're not going to tow in 6th gear w/ that engine.
Good luck!