Reduce Sway

The 26 foot TT didn’t wag the dog. A 37 foot TT with a light TV will...”rated” or not. Towing capacity goes to pulling power. I’ll bet you are over on payload. Care to wager?

HW 845
GVWR 9600
Dry 7245

The truck pulls the trailer with no problems other than sway in winds and Semi passing.

I'm not gonna get into a long explanation on towing weights but check into payload and tongue weight and get a better understanding of how it works. There is a ton of info on here about it. My guess you don't have the best truck for the job and that will be your weak point. The Pro Pride hitch will most likely help but if you are over weight you are over weight.
What are the trailer specs?

I am pulling with a 2018 Ford F150 5L, it is rated to pull up to 10,400.

What are you pulling with? That is a big jump in weight and length. If you have enough truck and some extra cash to spend look at the Pro Pride hitch. It's the way to go, and he might even offer a money back guarantee on it, at least 7 years ago he did.

Yes after reading today I have to make sure the bars are rated correctly for the TW. There is so much out there in the forums it's hard to know which one to go with..

The Dual Cam will help. First I would also play with adding more tension on the spring bars.
You wan't to stop the sway from starting in the first place as much as controlling it afterwards.

You could also weigh the tongue and make sure the bars are sized right.

I am in the same boat and just started searching the inter webs this morning!