Welcome and congrats on the 32 BHDS!!!
Go with the 14k Equal-I-Zer model. Or possibly the Reese Dual Cam or SC with the 1500lb wd bars. When I weighed our 32 (still need to reweigh) we had a 1400lb tw. Since then I have added shelves in the front and hall wardrobes, the vinyl fence post sleeve underneath near the front (have a 7' GPL folding ladder, sewer hose, and 4-6' pvc poles for a "tarp tent"), and the factory rear cargo hitch (added afterward) for the bikes (4).
Having the 8.1/4.10 combo I don't see why you would have any issues with the 32 BHDS. Just let the motor rev if/when needed.
Check your factory hitch on the Burb. With a higher tw and a round tube receiver hitch, you may want to consider replacing the factory hitch with a nice square tube model. Round tube hitches can "wind up" or twist when latching the wd bars up, especially with a higher tw. There are also reports of the factory round tube model failing where the receiver tube is welded to the cross tube.
Plan on readjusting the wdh once you get the 32 home and all loaded up. The dealer is only adjusting the wdh for an empty trailer.