The Eagle 339FLQS
frount living rooom may be a good fit for your truck. The 339FLQ has a spec'd dry pin weight of 1,965#. And 20% of it's GVWR is 2,520#. Both within your sticker 3,077 lbs payload capacity.
I think the North Point and Pinnacle front living rooms may be too heavy for your truck. The Pinnacle 38FLSA has a spec'd dry pin weight of 3,095 #.
However, from my experience, the sticker payload capacity is never correct.
I would suggest taking your truck, loaded as it would be for a camping trip and get it weighted at a CAT scale, getting both front and rear axle weights.
This way you can compare these weights against your truck's GVWR and Rear Axle GAWR and know exactly what your payload capacity is.
Don't forget to add ~200 - 250# to your weights for a 5th wheel hitch.
I would guess that the weights of the 339FLQ would be within your capability.
Hope this helps.