My 26BH weighed 6200 lbs with 720 lbs on the tongue the last time I weighed it. I have used three WDH setups on this rig: 1200 lb Husky Centerline, 600 lb Equal-i-zer, and a 1000 lbs Blue Ox.
I didn't like the Husky much but it handled the load fine though somehow I bent one of the bars. The 600 lb Equal-i-zer really had to be cranked up to work well. I definitely would have bought the 1000 lb version given the choice (I wasn't). The 1000 lb Blue Ox is my favourite and handles the load very well. I have to crank the bars up a fair bit so I think that going to the lower rated model would be a mistake.
Anyhow, why is your dealer basing any kind of towing decision on the dry weight, an almost useless number? They sound clueless. Your trailer will always, even when completely empty, weigh more than the dry weight. Your traveling weight is considerably higher than the dry weight. A very good rule of thumb is to base all your towing decisions on the GVWR of the trailer. This will account for trailer, loaded items, added options, and a reasonable safety margin.
2012 F150 5.0 litre
2013 Jayflight 26BH