I ordered my PCB through OSH Park.

The board came out very nicely, but I did notice one error I made. Several of the footprints were custom made, including the supercapacitors. For these components I only considered the pad dimensions, but not the full package size (which is wider than the pads).

I was still able to fit two of the capacitors on the board, and further added to this by stacking another two on the first ones.

The first tests seemed to work as intended, but after being removed from the charging coil, the LEDs would go dark, and a few seconds later turn on again for only dozens of seconds. I had not considered in designing that the charging circuit would be back-fed by the capacitors and waste the energy that was just stored. I added a diode in series with the 5V coil output to stop any current flowing back to the charging module. This solved the issue and allowed for much longer operation time.