How strict do you want to follow stickers on your truck? I have the exact same truck - you can carry much more weight.
Your rear axle is rated for over 9000lbs. The limiting factor right now is your rear tires. Assuming you have the stock Dodge/Ram tires and rims at 265/70/17 and 3195lbs each. Your rear axle is now tire limited to 6390lbs. 6390lbs (two tires) - 2980lbs (rear truck weight) = 3410lbs. At this point your suspension will be a bit of a weak point but you've addressed this. You can carry 3410lbs. I'm waiting for a GVWR proponent to come out of the woods here but many will agree with me. You can probably carry a little more as the front axle will take a little weight but I really wouldn't count on that. Safe assumption is that all the camper weight will go on the rear axle.
I agree completely with your weights, my truck was within 40lbs.
If you upgrade tires and rims, you can carry much more.
Get the camper. It will carry fine. I like my similar Bigfoot.