That's the card's protection. You can't power it up until all pins are connected.
If you already have a "dual mini 6pin to single 8pin", you can get another "single 8pin FEMALE to DUAL 6+2pin". So that you can use them in combination to power your GTX780.
Thanks.
What would been the “correct” way to do this from the outset? A single 6-pin mini to 8-pin cable?
Would it be worth it to just keep using the two backplane connectors for the 8-pin port and tap a couple of SATA ports for the 6-pin?