your design should work just fine.glue up the all 4 pieces
clamp from top to bottom, 2 or 3 clamps per side.
make sure the box is sqaure. measure corner to corner and tweak the angle of the clamps until you get the same measurment.
glue and scew your corner blocks in now, dont wait!
chech for sqare again.
tips:
pre drill and countersink all holes in the blocks. the screw should slide right through the block. remove any chips/burrs from backside.
put all screws into the side first ( the piece with the "o")
then screw into the top or bottom, the screws will work with the clamps.
you'll need a slower setting glue like a liquid hide or a plastic resin. yellow glue will set too fast for you.
make sure your corner blocks are shorter than the sides. you still need the front and back to drop in.
other thoughts:
you could use this joint on the front and back too. in which case i would assemble the top and two sides with the corner blocks.
slide the front and back pannels in with glue.
then put the bottom on. now you can reach into the woofer hole to to get at the bottom glue blocks. now you have a great reason to get more clamps!