OR, you could make a jig out of 1" thick material that follows the frame of the front piece. Maybe styrofoam. Cut it to follow the contours of the front panel, place it on the bench, place the fabric on it, with the to be glued side facing out. Position and pre stretch the fabric on the jig so it lines up perfectly with the front of the faceplate on the cabinet. Do a few dry runs before you use the spray mount. Spray the ENTIRE front mounting surface. Use a light coat of spraymount so it doesn't bleed through the grillcloth.
Then, press the grillcloth into place with the styrofoam jig.
I like the substrate idea as well.
Veerry touchy work here...