I'm building a 20'x30' backyard entertainment room. It has 10' foot walls on 2 sides creating a L shape open room. I have 3 18" LVLs on one 30' side and 2 20' LVLs on the 20' side. The corner of where the LvLs meet is supported by a 5"x5" 3/8" thick square tube with 1'x1' plate on bottom on my concrete pad and also supporting the corner of the LVLs. I cut the 30' distance by also installing 2 18" LVL parallel to the 30'. I have installed 2x6 by 15' with hangers stretching to the the walls on 24" on center. Will that support 1/2" Sheetrock or wood paneling without bowing down?
regarding the 2x6 joists. a 15' foot span is excessive for 2x6's even just for drywall i would nail vertical 2x4's to the sides of the 2x6 tying them into the rafters to help reduce sag. if you do this though i would run a dryline across the underside of the 2x6's and use a feeler block to make sure the 2x6's are running flat.. any major variations in height in the 2x6's will telegraph through to the drywall
I can't say that I understood much of your description of what you are building but here is the IRC joist span table for ceilings with no attic storage and 5 PSF for dead load and 10 PSF for live loading.