Nothing is going to handle 40 mph crosswind well. Every truck and trailer combo I've had was white Knuckled with 40 mph crosswinds with Reese Dual cam or Blue Ox hitches.
It's not the sway but the push and pull of the whole rig from the gusts pushing then stopping. The oscillation of the pushing. With soft, cushy side walls of P-series tires, your truck will wobble back and forth. With the large side surface area, a travel trailer is about the worst trailer to have in wind gusts.
With E rated 10 ply LT tires, the stiff sidewalls of the tires will minimize greatly the wobble effect of the sidewalls, and make the truck much more stable but the rig will still be pushed from the gusts.
The problem is when the driver reacts to the push and as soon as the gust is gone, the driver needs to react as well. This constant reaction, if over done, can result in driver induced sway.
All said, my 2016 Aluminum F150 with the Blue Ox Sway Pro hitch offers a better and more stable tow with P-Series tires than my previous 2012 Steel F150 with the Reese Strait-Line Hitch System (HP Dual Cam).
None the less LT tires will make the tow much much better as I've experience when I went to E-Rated 10 Ply LT tires on my previous 2012 F150.
Living in Northern Indiana we have high wind gusts all the time. Mainly coming off of the lake (Lake Michigan) and no obstacles to break up wind coming across open farm fields.
I will say we just had 50 mph gusts and several roads were closed last weekend to semi truck/trailer combinations due to it. I of course was pulling my trailer right off of the shore of Lake Michigan which was at it's worst.
Driving between 45 - 55 mph, it was none eventful. Pushing me, yes, but not to an unsafe level. I definitely wouldn't tow above 55 mph with gusts that high.
2019 Ford F150 XLT Sport, CC, 4WD, 145" WB, 3.5L Ecoboost, 10 speed, 3.55 9.75" Locking Axle, Max Tow, 1831# Payload, 10700# Tow Rating, pulling a
2020 Rockwood Premier 2716g, with a 14' box.
Previous 2012 Jayco Jay Flight 26BH.