Well this is one of my hare-brained schemes that didn't die on the vine. I took your advice and made some tweaks to my design, mostly the addition of some pegs for extra structural support and from that drew up my design properly and made a maquette to check I was happy with it:
I actually made a couple of maquettes because I learned from the first one that by offsetting the slots top and bottom I could create a single design that could be configured in multiple ways. Having had a chat with the Epilog-equipped cutting folks at
Cutlasercut in Hackney I learned that they could not cut one piece of 12mm plywood as it's too thick so I opted to cut 2x 3mm sheets and a 6mm sheet of MDF and from that I could glue the MDF into a plywood sandwich. I went and picked up the cut pieces on Friday and did a test assembly:
You can see the pegs I added to the design for rigidity here:
I was pretty happy with this. The laser cutting process is so precise that the pieces locked together absolutely perfectly with no extra sanding or cutting required. I glued the plywood/MDF sandwich and reassembled the rack and put a couple of coats of varnish on it yesterday. I'm still deliberating if I want to paint either the sides or the cross-pieces white for a sort Dieter Rams era Braun style finish but that's a decision that can wait a while.
Here's the finished rack:
And here it is in situ:
I'm really pleased with this, it's very sturdy and matches the style of our living room as well as a guitar rack could I think. I need to clean up the vector drawing file and add some notes but I'll post the finished plans in an Epilog friendly file format in case anyone else wants to get this design cut for themselves. Hopefully that will happen this week work permitting.