So I measured the thickness of the black acrylic sheet I’m using for the Totally Featureless clock and machined the rabbets to match. Went to assemble everything and the rabbets are too shallow!
Come to find out that the sheet varies in thickness from about 0.437 to 0.475 across the four pieces I’d cut and, of course, I’d measured the thinnest end of the thinnest piece. Makes no sense to me, as I’d expect the thickness to be pretty well controlled over a few feet of sheet, but that’s not how things went down.
The simplest solution was to mill a flat on the inside of the case to match the rabbet, so all four panel ends were the same thickness. The sketch below has the straight dope.
Milling with a 3/8-inch end mill at 2500 rpm, 10 ipm, in one pass with no cooling was OK.
I’ll insert some brass shimstock into the rabbets to make the outside edges wind up flush.
The Smell of Molten Projects in the Morning 
Same problems here in India, I was making some iambic keyers from using acrylic and found that sheets vary in thickness a lot.
I don’t know what you use to glue the bits together. Here a local acrylic specialist showed me to dissolve fine bits of clear acrylic in chloroform and use that as glue. You can control the viscosity to suit your job. Works well.
sheets vary in thickness a lot
As they say, measure twice, cut once!
what you use to glue the bits together
I used clear epoxy, which formed a mechanical (rather than fusion) bond and filled the voids around the brass shims.
Epoxy should work well in this application, because it’s a low-stress job: a box hanging on a wall under a kitchen cabinet. Not appropriate for, say, an instrument case…
dissolve fine bits of clear acrylic in chloroform
Not the sort of chemical we can get off the shelf around here. I’ve read of similar concoctions using acetone or MEK, but I generally use Plastruct, a commercial solvent adhesive, for smaller projects with better fit-up.