Although I am confident you could get a SRW to safely tow that weight with modifications, I don't feel in OEM trim it can be done safely. If you already owned the SRW or plan to make one or two tows a year, it may make sense to go this route with a used SRW.
On the the other hand, I would not go purchase a new truck and exceed its rating during the warranty period or "under buy" for my intended purpose. There is too much money spent on a new vehicle to possibly negate warranty coverage.
My F250 commonly carried 7000-8000 lbs on its rear axle after I switched from a toy hauler to a truck camper. It did this well for 10K miles each year but was finally sold when I decided I wanted an additional ton of payload to the 4000-5000 lbs I was already carrying. Knowing my intend use, I purchased a truck with 9000 lbs of payload capacity to handle my projected 7000 lb load this Spring.