A VERY quick drawing and I spaced everything out a bit and didn't include dimensions. I wouldn't make a face that large out of acrylic myself, but I guess it depends on what you have available. You will need to make the can a bit deeper to account for the hanger bar. BTW, if you drill oversized holes in the acrylic you CAN screw it to the cabinet, but again I'd do it out of polycarb. Depending on your sheet metal brake, I'd actually go to .080" thick aluminum but it gets hard to bend in 9' lengths, though it could be pieced. Use a Lord's type adhesive (or channel bond) and don't just rely on the regular acrylic glue to hold the hanger bar to the face.
I've been building electric signs for WAY too long and even though an extrusion kit is expensive you save so much time on fabrication that it's usually well worth it.