Step 5: Laser cut the santoprene and glue it on
I ordered 6 12"x24" sheets of 1/16" Santoprene (a type of rubber that plays nice with laser cutters) and made up a pattern of slits in Corel Draw that matched spacing of the holes in the acrylic and that could be tiled easily so that I could use multiple sheets of my 2 sq. foot rubber to cover the entire area of the Lite Brite.
Once the file was done, I laser cut each of the 6 sheets with the pattern and glued the sheets behind the front layer of black acrylic using the special cancer causing industrial adhesive - Devcon Rubber Adhesive 14900.
I crudely rolled the adhesive onto the back of the front black acrylic sheet, so as not to get it on the parts of santoprene that would ultimately show through the holes, allowed it to dry until it was tacky, and then put the santoprene into place and applied pressure until it set.
I found that putting a small section of an adhesive roller onto my own applicator - in this case a cardboard tube - was more effective then rolling it on using a conventional paint roller.