AGHHH I had a nice writeup and cntrl A'd it to death.
Anyhow, i ran into this on my first trip with a 28' Coleman. I also have a F150 Screw with the short short short bed. I had annoying sway, but the winds were up to 30MPH gusting.
Turned out that bars weren't tight. When I first hooked up it looked like the trailer was too nose high, and I didn't have a level with me to check(though should have just bought one). I weighed the rig when I left the dealer, and then weighed the truck later(yesterday in fact. The front was light by 180#, all the TW was on the hitch at the tune of 840#. All this led to sway with the cross winds.
First for your truck, not knowing the tire size, will have to suggest. Set air pressure front and rear to 40 PSI, I have 20's on mine, and are P rated not XL. Equalize the pressures between front and rear for best stability.
Second, go through the manual step by step, measure everything twice on level ground. Go by what the hitch manual says, not the truck manual, reason being, the hitch manufacturer does testing on many vehicles, and if they found that the truck manufacturers statements were better than theirs, they would say so in the manual. It is also what they came up with from their testing.
Third, weigh it, weigh everything. Verify that you are transferring TW to the front axle. The thing I found is that after weighing it when empty, I heard DING DING DUMMY! That's why I had sway, the hitch wasn't doing its job. Knowing the weights is 2/3rd's the battle
Fourth, add a second friction bar, one is not enough for a long trailer with the 145" WB F150. I added one just today, and if I find I still have sway(which I am pretty confident I cured), I will add a second. My trailer is 7600# GVWR, and is about 5100# dry when I brought it home. I also have a 19' Horse trailer that I tow occasionally, and never had sway with it because it was setup by the book. I also tow a 6x12 V nose enclosed that is 8' tall, and last weekend a trip to Iowa on very windy days I had a touch of sway with it, but just enough to let me know, hey its windy back here. It is a standard 2" hitch, but well balanced
As far as the electronic sway control on our trucks, they only work when the truck detects an imbalance, and applies braking and engine management to reduce the sway after it occurs, and has zero effect on active sway control. When it happens, you will know as the dash will light up and alarms will go off, at least that is what mine does, tested it out one day with my little trailer.
From your description, sounds like you didn't have enough tension on the spring bars, and since you say you can't get them up to the tip up, I would suggest taking the hitch apart, measure everything twice, and reassemble by the book. Your head is tipped too far back causing the bars to be too far down. Don't be fixated on having the bars parallel with the trailer frame as sometimes, you wont be able to get them perfect, and it is better to have more pressure than not enough. It is said to have the hitch 1" higher on the TV than the socket on the trailer, but if you can't get it, go lower than higher as the higher setting would put it exactly where you describe yours at, bars too low or too high. Sometimes no matter how you set the shank, it just wont line up, you need to be 1/2" higer or lower and can't get there, so take the lower measurement. Thats how mine is setup and on the HT its perfect, and I believe it will be just as good on the TT. It's OK to have the bars up a little and have a slight bend if you can't get them parallel. Everything you described to me sounds as if the hitch needs to be reconfigured. Try that before throwing any more money at it.