But, it wasn't quite enough.
Enter the laser cutter...
Step 1: Planning
I worked on squared paper, planning routes up and down through five layers. I exploited the squares' size to plan 20mm channels, allowing both one cent and one penny coins to be used in the maze.
I then scanned the sketches into PDF files, and used InkScape to "draw over" the PDFs, and save the digital versions as DXF files.
Step 2: Cutting
The former was the closest available thickness that would allow the coins to move freely, the latter was the thinnest acrylic available, to keep the bulk of the maze down a little, and to stop coins falling at an odd angle and getting stuck.
I used an Epilog laser cutter, at the setting recommended by the operating manual for the materials.
I left the protective film on the acrylic during cutting.
Step 3: Assembly
A word of warning: if you are using my files, check the bolt-hole alignment - as a result of them being basically hand-drawn, some of the holes needed a quick go with a dremel to round them off and line them up.
It is important that I held the layers together with bolts, rather than adhesive, because the square section in the lower layers is a trap - if your penny ends up in there, you have failed, and can only get your money back by dismantling the maze.