You're over the payload of all the trucks you're looking at. That's before you add any truck accessories, pets, gear, or hitch up a trailer.
I carried a 4,000 pound camper on a 3500 reg. cab SRW for thousands of miles. I was about 1,200 pounds over the GVWR. Then I put it on a dually. By the time I drove down my driveway and onto the road I could tell there was a lot less bounce and sway on the dually. The dually, being a crew cab and also having a flatbed with tool boxes, is about 1,700 pounds over it's GVWR.
So yes, you can certainly run over the GVWR as long as you don't exceed tire and axle weights. But, there's no reason to start with a truck that you already know is too small for the job.