Whether you work with Superior, Gemini/Showcase, or a local acrylic fabricator, you'll want to specify that they bond strips of acrylic around the outer perimeter of the open side, about 1/4" wide and as tall as the frame's rabbet after the mountingbacking boards are in it. I suggest black for "The Edge" because it is not as visible through the front of the acrylic box.
Something like this:
|
|
|]
And when you build the frame base for the box, be sure to measure not the rabbet dimensions, but the "sight" dimensions -- remember that the inner edge of the frame will be outside the box.