Suggestion
Step away from the brochures. You are confusing yourself with all the charts. Please, just ignore all the info about max towing, because you won't get there, and if you go by it, you will exceed your trucks capacities.
Weigh your truck with you and your wife in it, and a full tank of gas. Get separate weights for front and rear axle.
GVWR is 10,000 for your truck. Subtract your actual weight from 10,000 That is your remaining payload after you, wife, and gas. Some of us believe 3/4 tons are artificially capped at 10,000 GVWR. Others won't take a Big Mac to go if it puts them over 10K. Your payload should be on the yellow sticker on your door jamb. That's the payload for YOUR truck, not a brochure number. Which is what you need.
Payload is a good number to have. But, for 5ers, many of us use the axle weight as the critical number to follow. Even on my 3500, I exceed my payload by 10lbs, but have more than enough axle capacity for my 5er.
After you weigh the truck, you will have a rear axle weight. Look on door jam for GAWR rear. It will should say 6000. Subtract your rear axle weight that you got at the scale, from 6000. That is the MAX pin weight you can handle with your truck.
Generally speaking, you should use the trailers GVWR x 25% to estimate a trailers pin weight. If you find a trailer you like, look for the GVWR sticker on the drivers corner of the 5er. Multiply that by .25 to get your estimated pin weight.
Don't forget to take into consideration the weight of the hitch. 2-300 lbs depending on what hitch you get.
If you cannot weigh your truck, the previous chart can help. Looks like axle weight is neighborhood of 2900lbs. I would go with 3000. 6000-3000 is 3000 remaining axle capacity. Estimate 300 lbs for hitch (to be safe). Your pin weight cannot exceed that number (2700), which puts you in a 12,000 lb 5er category at best.
There is no way I could see you towing a 16,000 5er with your truck. It should/will likely have 3500-4000 pin weight.
Mike