Not surprised by the initial 1,300lb tongue weight for the 306RKDS (9,950lbs GVWR)...., and I agree your present WDH rating of 1,200lb isn't a good match for this TT.
Your "as shipped" from the factory probably has a UVW around 8,200lbs (yellow sticker).
Hypothetical loaded 306RKDS, "no fluids
": (UVW 8,200lbs + Cargo 1,000lbs + Dealer 75lbs) = 9,275lb loaded weight
Desired loaded tongue weight: 9,275lbs = 1,206lbs - 1,391lbs (13% - 15% of gross)....., and 15% is more common with the heavier and longer TT's (also enhances TV handling). Also, if you normally travel with a full fresh water tank the added weight (630lbs) and location of the tank will have to be considered.
My prior Eagle CAT scaled with a loaded tongue weight of 1,300lbs (15% of gross) and I had/still use a Reese Dual Cam (Strait-Line WDH) with 1,500lb spring bars...... towed great.
IMO 1,400lb rated spring bars would work, but you would have to watch your TT loading habits. A WDH with spring bars rated in the 1,500lb - 1,700lb range would be ideal (Reese has them).
CAT Scale how-to: https://www.jaycoowners.com/forums/f...v-tt-3871.html
2016 GM 2500HD 6.0L/4.10
2018 Jay Flight 24RBS
2002 GM 2500HD 6.0L/4:10 (retired)
2005 Jayco Eagle 278FBS (retired)
1999 Jayco Eagle 246FB (retired)
Reese HP Dual Cam (integrated sway control)