I have the same truck and my Bigfoot is 4,000 lbs. I would be okay with a heavier TC. I am not a member of the Weight Police.
Keep in mind, not all of the same trucks have the same suspension. My '04 3500 has upper and lower overload springs. I did add a rear sway bar. Not really mandatory, but did reduce the sway. The previous owner installed Stable Loads. They reduce the amount of squat. I added air bags, but only use them for leveling side to side. They will help if I ever haul a heavy trailer with my TC.
I would ignore the bed damage.
