Oh I missed the part about the super heavy duty tires you put on.
You're fine, your truck is probably more capable at this point than most people's camper trucks are.
Your truck does indeed have the same axle as an F350, all the stuff you said the Ford people told you is right. A rear sway bar might be a nice thing to add if you haven't got one, there's an outfit called Hellwig that makes good ones, I use one myself. They don't cost a lot, there's really not much to them, and it'll help control the side to side sway.
And yes, I've been to Burning Man since back in the '90s, that's the primary reason I have a camper.
My avatar photo is my rig on the way there, that big cabin cruiser boat behind the camper is actually a land vehicle, what they call a "Mutant Vehicle". No longer seaworthy but it does a whole lot better on the desert than most people's boats do!!
Belly bars... those are a metal bar, usually square-tube, that goes under your truck from left to right and has brackets to attach it to the frame. Then you attach your camper tie downs to the ends of the bar. I love those, they're simple cheap easy and super effective.
This website appears to show them being available, for some reason they're hard to find.
http://www.billisrve.com/display.php?catid=1They're pretty easy to make though. Torklift's price is crazy, I'd sooner weld up my own set.
Now if you really wanna know the ultimate best and BY FAR easiest way to deal with a camper, here's what I did. I searched until I found a deal on one, the price new is steep, but it's a total game changer:
https://youtu.be/xOy5VoYg8Xk