After all the work, my Nyan Cat is now running on an actual Supercon badge, running the default firmware which will be part of every 2018 Supercon badge. Woohoo!
This specific unit of hardware actually has a minor assembly error: one of the battery trays is installed backwards. Here’s a picture of the back – both springs should be on the bottom, so both batteries have their positive end pointing up. The battery tray on the left is reversed from the way it should be.
The correct fix is to desolder the battery tray and solder it back on in the correct orientation. The simple hack is to jam a battery in there in the correct electrical orientation but against the tray orientation. Since this is a common mistake, the tray actually has a guard against reverse insertion. There’s a small plastic nub to prevent electrical contact if a battery is installed backwards. This nub allows the protruding positive end of AA battery to make contact, but keeps the flat negative end from making contact.
Side note: When equipped with protective battery tray like this one, putting a battery in backwards is a valid way to stop battery power consumption, because it opens the circuit and no current will flow. However some people have gotten in the habit of reversing batteries to deactivate electronics with or without this nub. Without this nub, they risk cell voltage reversal and damaging the battery. It makes me wince to see it.
But back to the badge: since the correct battery orientation in this case is reverse of tray orientation, the expedient hack is to snip the nub away with some tools and insert the battery “backwards”.
It’s a hack and it works.