I thought the F-150 Ecoboost with the max-tow had a little higher "payload capacity" (2,550lbs ??), but I will assume it is 1,740lbs per your post. Also, the TT's 930lb tongue weight is a "dry" (unloaded) specification.
The Eagle 314BDS has a UVW of 7,465lbs, add 350lbs for actual ship weight, add 125lbs for battery and WDH, and another 800lbs for "stuff" (not including fluids in the tanks). The "conservative" sum total would be a loaded TT weight of 8,740lbs
(GVWR of 9,975lbs). The desired loaded tongue range would be 13% to 15% of the TT's loaded weight.., thus a loaded tongue weight of 1,136lbs to 1,311lbs
. This also implies that a WDH rated at 1,500lbs would be desirable, and that the loaded tongue weight is subtracted from the TT's payload capacity (less passenger and cargo weight as well).
If in fact your TV's OEM receiver is rated at 1,150lbs in WDH mode, then the receiver needs to be upgraded..., assuming that no other TV weight limits are exceeded.