I discovered a number of settings in PCB that allows me to route all 96 pins of a DIN 41612 connector on a single side of a two-layer circuit board. I had to set my trace size to 6 mil, and reduce my annular ring size to somewhere in the vicinity of 10mil. These are figures which OSHPark seems to support, so I don't think other PCB fabs will have issues either.

I have many of the paths routed already. I just need to find an optimal layout for the rest of the circuitry. I really wish I didn't need a 74LVT20 or 74LVT04. Capturing and responding to signals on a card-by-card basis really ruins the elegance of the overall design, and appreciably complects the routing of signals. Thankfully I have two layers to play with.