A common problem is people view the Max payload as a fixed weight. Based on the specs for the 397
(Hitch
3,375
UVW
15,600
GVWR
20,000) your trailer weight will be between the last 2 numbers and can only be determined by WEIGHING your trailer.
Your truck's "listed" payload is simply the GVWR minus the actual truck weight (sometimes the manufacturer includes a driver) when it rolled off the assembly line. EVERYTHING else you add to the truck (people, tools, hitch, bed liner, bed cover, etc. reduces the listed payload value.
You specifically asked if your truck could handle a Fully Loaded 397 which would weigh 20,000 lbs. 20-25% of that weight will be seen on the truck as the "hitch weight". that means you will be putting 4,000-5,000 lbs of weight on your truck. You will definatley exceed the GVWR (max value the TRUCK is rated for) since as it left the factory it was only 3,701lbs away from the GVWR.
You don't list what the RAWR is (Rear Axle) but you are probably over that even further than you are over the GVWR. Rough math puts the weight your rear axle will be carrying at
(12,100 - 3701 = 8,399lbs for the truck alone as it rolled off of the factory floor. split approx 40/60 between front and rear and your empty truck is Add in 4,000 lbs hitch weight is at approx 5,040. Add in the 4,000 lb hitch weight and you are approx 9,040lbs on the rear axle (some will transfer to the front but not much) Add the rear axle's portion of the stuff added to the truck listed above and you are pretty close, if not over to 10,000lbs on the rear axle. Definitely dooley territory.
Bill