I've been watching videos on soldering each pin back together and that would be a last resort for me.  I've e-mailed Fat Shark and gotten no response (they've helped me with spare parts before)...I can't just use any 12-pin ribbon cable...can I? 

   

It doesn't look like a 1 to 1 direct cable. The trace in the ribbon looks custom.

That's a custom ribbon cable. Your only option it to wait for FatShark to get back to you or chase them again. If you happen to know who the authorised repair centre is in your country you can try and contact them direct instead because all FatShark will do is refer you to them anyway and get them to contact you, so you could try and cut out the middle man.

Bummer...Well, I e-mailed Fatshark, the repair center in my country and another one in the UK. Hopefully someone gets back to me soon.