The brochure says the TT tires are LRD. If so, I would run those at max. sidewall 65 psi.
The tongue weight seems rather light at 620 lbs. The factory hitch wt. is 580 lbs and you would expect TW to go up a lot more than 40 lbs. As you mentioned, I would want to be more in the 12-13 percent range. Did you do a pass with the bars engaged and another pass with them dis-engaged. To get TW, you want the bars dis-engaged because the WDH transfers some wt. onto the trailer's axles.
The factory specs say the UVW is 5685 lbs with 7495 lb GVWR and you have calculated the actual TT wt. (GVW) to be 6080 lbs. That indicates you've only added 395 lbs of "stuff" in the TT for 2 adults & 1 child which can't be right. Typically the added wt. on top of the UVW is something like 600 - 1500 lbs. Unless I've missed something, I think maybe you haven't done 3 passes to get all the weights correctly?
Edit: I see you plan to go back to the scale for a 3rd pass with bars disengaged.
