Feeling road imperfections in steering wheel and steering wheel pulling over bumps

Hey all, my steering wheel is starting to bug me driving over back roads and bumps. I live in the countryside and when I drive over some of the bad bumpy ( no pavement missing just bad asphalt patches and depressions ) the wheel pulls back and forth a couple inches as I roll over them at 5mph. I don't have any creatable play in the steering wheel.
Driving around town over pavement seams also "bumps" the wheel either way depending on my approach, I can feel most imperfections in the road

Driving over gravel really gets it going.
I took it back to the dealership, it was certified used and only bought a couple months back so I'm covered for a year under the more comprehensive warranty.
They said they couldn't find any bad steering or suspension components and said it was probably my tires being too hard ,
I have westlake radial sl369 a/t 245/75r16, 30psi as the door sticker says they should be, 7in wide on a 7in wide stock steel rim. 500tread wear rating. Came on the truck when I bought it.
Can anyone confirm if the tires are the likely culprit? Is this considered normal operation? My fathers truck and suv don't feel exactly like this , it just feels off to me.
And if it is, what tires could be better for me?

Everything is stock, 2015 v6 double cab, base model, 55k miles

 

Do you have any current alignment numbers. Bad caster might cause your issue as well as tires.

 

Your experience is consistent with my 2006 double cab with 186K miles. Driven a lot on washboard roads in beach community every summer for many years. Steering wheel vibration and motion sucks.

 

I don't but I do plan on getting an alignment soon, It drifts a hair to the left but almost unnoticeably so. I'll have to see about caster , thanks

 

What is the load rating on the tire? It appears Westlake makes 245/75/16 and a LT 245/75/16 (which is an E load rating with 10 plys).

 

I don't believe they're the LT , i don't see an lt on them nor do I see a letter for the load rating (unless I'm just that blind) , just
245/75/r16 111S M+S in small font and
Just westlake radial sl369 a/t 245/75r16
In large font. It does list Max load 2403lbs at 44psi by itself on the side wall.