Are you talking about very flat, white vinyl-like plastic covered ribbon cable or about softer, multi-colored or grey ribbon cable? If it is the white flat stuff, I would desolder the connector and solder directly in, no connector, the softer multicolor cabling. Notice though that the capacitance between the conductors might end up being different enough to cause some electrical noise, depending what modules they interconnect. The routing might be important too.
If you are uneasy about desoldering and resoldering on PC boards, then yes, try to find the same kind of cable and, if they are still not long enough, maybe solder these end to end? (and cover with electrical tape!)
post a picture (good enough to be able to count the wires!), I'll look if I have anything in my numerous junk boxes, and if yes, I could send them to you.
This said, can you stack the boards on top of each other, with spacers in between? Flip them, rotate them?
At ISE, on the DART ROV's we used to cut off the Panasonic camera PC board, separating the video amplification from the power and transmission section. Just hacksawing through them, I was in disbelief when I was instructed to do that for the first time! Then we just jumpered the two section together, the video amp being mounted with the camera tube (!) on the pan and tilt unit, while the rest of the board sat back in the main enclosure. No problemo!