I got the PCBs designed in a single evening and quickly sent them off to China for manufacture. They've arrived, and turns out there's a bit of a problem: I'm a dingus.
The first problem is that one of the pins for the nixie tube was never actually routed to its corresponding header pin. So that digit doesn't work at all.
The second problem is that I put the footprint for the nixie tube upside down. So in order for the board to work, it has to be placed upside down. Not very convenient or aesthetically pleasing.
So I've fixed the board and sent the order off to be manufactured.