Hi Ethan,
Just a thought for everyone but just need your approval :-)

Using the 1 inch wide 1/4 inch thick strip of wood. I was wondering.... If I drilled holes in places on the strip of wood and glued in the holes some dowling, making it come out about 4 inches (the thickness of my mineral fibre)
Doing this for both strips of wood, creating platforms for the 2ft x 2ft panels of 4 inch mineral wool to sit in,

As long as the mineral fibre panels touch the strips of wood, and are held tightly by the dowling, would this be a solution for straddling the corners with mineral wool?,

Just that I don't want to poke holes in the fabric through to the fibres, just in case of spills, I'm extremely allergic to this stuff.

Anyways, let me know what you all think :-)

Jason.