Complex idea: Two PCBs in parallel. Mount standard chassis-style BNC into a big hole on one board (perpendicular to the PCB, as if it were a chassis). Solder the center pin into a small hole on the other board.
Interconnect between boards might not be nice, but you also might be able to get away without making a case if you put some small feet or a 3rd dummy PCB as an insulator on the bottom board.