Please verify the axle ratio per RPO code in the glove box. I believe the HD towing package includes 3.42 axle and trans cooler, but I know it does not include the 3.42 axle on the 1/2 ton pickups. While the 6-spd trans with 3.08 gear is slightly better than a prior 4-spd with 4.10, GM still limits to 5k pounds. The 6-spd/3.42 combo will work very well. Plan to use tow/haul mode and limit the trans to 4th or 5th using the manual mode.
No reason not to still keep your hopes up. There are plenty of BH TTs under 6k dry, especially if you can skip the outdoor kitchen.
In addition to that Bullet 286, Coachmen Freedom Express 292BHDS, Forest River Surveyor Select 294, Rockwood 2905, 2907, 2909 are all good examples.