My TT has a GVWR of #5000... Towed it with a 97 F150 with the 5.4 in it and it did pretty good for the most part...
I only had the 4 speed trans and 3.55 gears, but I was in 2nd gear on most grades over 4 percent.. Towing on the flats, 3rd was best for all around towing. It would go into 4th going down hill or on the flats with a tail wind.. ;)
But, it towed it comfortably, no sway, no worries.. Just had to deal with the high rpms.. Not a bad thing, really, but....
Then I got my current F150.. Tow the same TT with it and OMG... What a different towing experience it is..
My wife and I can actually hear the radio or carry on a conversation while pulling a grade now.. I have never had to 'mat' the gas pedal going up a grade, or just trying to merge into traffic with the new truck.. With the old 97... Well, that pedal went to the floor at times..
JMO, but I'd stick to something in the #5000 GVWR for a TT with the 4.6...
Good luck!
Mitch