Another way to do this is to
-make a backboard from 3/8" coroplast (if your item is larger than 4'x8' the coroplast can be spliced using vertical flutes (they fit into each other) and joins reinforced with Lineco frame sealing tape. 3/8" is pretty rigid, but If you need more rigidity the coroplast can be attached to a cross braced wooden strainer (bass wood is a good choice if available) or laminated to a second sheet of coroplast with flutes perpendicular to the first sheet. The weight adds up though.
-cover the coroplast with needle punched polyester (not the puffy kind- one trade name is insulate, quilting shops carry it, it is about 1/8" thick)I use 3M#415 tape or Beva to attach it either to the front edges or wrap around to the reverse.
-cover that with your washed show fabric, wrapping edges to reverse and Bevaing down
-center textile and stitch down with curved needle. Depending on weave, you might be able to use standard curved needles, or if very fine ones needed ou can order from Fine Science Tools.
The benefit of this is that there is a solid backboard, so no air filtration.
If it is to be glazed with Plexi you can also make this into a pressure mount and reduce sewing; so many possible variations!
Plywood is not a good choice as there will be a lot of acidic and other volatile vapors emitted by it and absorbed by the textile. I have a Miro print in now that has a very strong plywood pattern burned into the reverse.
Rebecca