I tow a smaller TH with my F250. Yes, there is a slight drop in the pin weight when I'm fully loaded in the back. But its a minimal drop in the big picture and not going to get you any where close to being within your trucks capacity. With my 900 lb Harley and my 800 lb ATV both loaded in the garage, my 2140 pin weight drops about 40 lbs. I also find that the pin weight is effected slightly by how level or out of level the rig sits when hitched up. I added rear air springs on my truck to help keep it level.
Its primarily a personal choice so you'll hear lots of opinions; some want to be 20% under the rated capacity and some are OK being 20% over the rated capacity. I don't try to change anyone elses mind, but I try to stay within the mfg's rated capacities for my rigs. That was hard to do with an F250 and its 10,000 lb GVWR, even though my axles (6000 + 6200) and tires were rated for much more.
Once you're truck is loaded for travel, you're going to need something closer to the 2000 lb pin weight, rather than the 2400 lb based on the sticker "dry weight". That severely limits your choices.
