After a recommendation on this forum, I've been using the old 40 pin IDE cables (not the 80 way newer faster IDE cables).
At the Mega end I break them out into a 20 pin header and solder the wires to each pin. At least I've only got to do this on one end.
I also wire the upper / lower pins for each row together, that way it doesn't matter if I plug it in at the display using either row.
Iain