The project recommends:
"It is strongly recommended to protect the signals from the instrument, in case of an accidental short or similar. On the +5 volt feed, use BAT41, BAT42 or other low voltage drop diode, or at least a small fuse in the 100-200 mA range. On the signal wires, VFDSCLK, VFDSIN, VFDSOUT and VFDSEN, use a resistor in the range 1 kOhm to 3.3 kOhm or so."
Since you only need to expose VFDSCLK, VFDSOUT, and VFDSEN, I'd buffer them each with two inverters in a 74LS|HC14 + 330R on each output. Or similar buffer chip: '04, '08, '244, '245, etc. I don't know what connector you'll be using but you could mount the buffer chip behind it (on a small perfboard, PCB) or in-line between the wires to the connector from the J1 (on the display board).
See below for a partial schematic of how the VM COMPLETE output on my HP3478A is protected. Note the reversed protection diodes to +5V and GND. I can't advise on TVS diodes as I've never used them.