It appears the top piece (page 9) would be 1/4" hardwood. The bottom piece on the same page is 1" thick hardwood as well.
It does appear the top piece is required to make the acrylic stand up straight.
If you have a band saw you could do this out of one piece of hardwood 1 5/16" thick. You would cut off the top part at 1/4" then proceed with the rest of the instructions. By gluing the top back on and sanding the edges, you could make it look like it was one piece of wood only!
I hope that helps.
Karl