If you get the 703 FRK with the paper/foil backing on one side, and turn that side up toward the ceiling...it probably will not sag much...though TBH, with any of these products, 703, Roxul, even the cotton fiber ones I would want some kind of frame, and most definitely some sort containment material. Very porous burlap and other types of open weave material, even the Guilford of Maine stuff...is still porous enough to let fibers fall through, especially from ceiling mounted traps.
All insulation products can cause irritation, even the cotton stuff (try inhaling some lint from your dryer lint trap).
I would at least double wrap them...a layer of polyester felt cloth, plus the outer "cosmetic" layer. The ones I made recently, I even wrapped the 703 in a layer of 0.4 mil plastic, so the 703 is completely sealed, and that thin layer has basically zero effect on the acoustic properties.
The ones that guy built in the video...TBH...they look pretty shabby. I mean, all that work, and you can see the droopy cloth surface on some of the panel. You need to use a polyester material, as it will not stretch/sag with environmental changes like cotton or other moisture absorbing materials can.
Not to mention, for that small room, all those traps made it look like one of those padded nut house cells.
I'm sure it works OK...I just thought for the amount of work and expense it ended up looking kinda throw-together.
Here's the ones I built recently....they were meant to be mobile and not for permanent mounting, more for multi-use, and they are self standing.
Bass Trap Madness