I'll start by showing you the result:

Now I'll tell you how I got there. Here is a rough sketch of the idea.

I started with a little scrap of plywood. This was just a proof of concept and won't actually be used, so I wasn't overly concerned with details, but it came out much better than I expected. First I cut out the design with a scroll saw(homemade saw, but that's another project). Then used a router to make a void in the back. By the way, that's the Japanese character for "do" as in the musical notes: do, re, mi, fa, so, la, ti.

I'm using nice poplar plywood that is sooo nice to cut. Anyway, then I set it face down on some silicone baking sheet and carefully, to avoid bubbles and empty corners, filled it up with hot glue.

After giving it plenty of time to cool, it lifted right off the sheet and looked like this.

Then it was time for the hard part. With tweezers and a way overpowered soldering iron I managed to attach four smd LEDs to some magnet wire. I somehow managed to get them all successfully connected in the right orientation on the first try. Then I tacked them on the wood with hot glue.

Here they are with about 50mA going through the set in parallel.

I taped some foil onto a piece of milk carton and set the device on top. The result was fantastic. I'll be using this method for the final product. But I'm not looking forward to cutting out some of the more complicated characters. I need: ど　れ　み　ふぁ　そ　ら　し . I think ふぁ will be a nightmare, so I might just cut the ふ part and paint the other.