The same signal routed to the headphone jack is routed to the coaxial digital output if you can use that. Set the digital out format to SPDIF or AES in the I/O menu (D.OUT SEL). But presumably you'll use a pair of the analog RCA outs to send the mix to the camcorder. To do that, set (A.OUT SEL) in the I/O menu to MIX instead of DIRECT. The same mix is then sent to each RCA out channel pair, doesn't matter if you plug into ch1&2, ch3&4 or ch5&6. Stereo left = channels 1,3,5 and stereo right = channels 2,4,6
Use the DR-680's mixer to configure each channel's level and panning position as appropriate by selecting each channel individually and adjusting LEVEL and PAN using the controls on the front panel. You'll probably want each channel hard-panned to either left, right, or center, which can be set beforehand. You can guess at mix levels beforehand, but you'll probably want to adjust those at the gig, wearing highly-isolating headphones to monitor what you are doing as best you can.
Remember that excluding your record-trim gain for each channel, which obviously affects output level as well as the recording level, there are 3 separate points of level control determining what you are hearing in the monitor mix over the 'phones: 1) the monitor LEVEL of each individual channel, determining how much of that channel is sent to the stereo mix bus; 2) stereo mix LEVEL, controlling the output level of the stereo mix bus; and 3) the headphone output level, which adjusts the level of the headphone amp.
Once you have your channels balanced with each other as you like using the LEVEL control for each channel, you can adjust the output level of the entire mix using the stereo mix level. Stereo mix level controls output level sent to the RCAs, the Digital output, and the headphone amp. Start with the stereo mix level all the way up. Turn it down as needed if you need to attenuate prior to the camcorder's input. If you are running very close to clipping on several channels which are being summed together in the mixer, then you should turn the stereo mix level down slightly to avoid digitally clipping the mix bus after the channels are summed.
In a pinch you can use the headphone output to the camcorder, but then the headphone level knob is also in play, and the output from the RCAs is cleaner and more appropriate. The digital out is the best choice in terms of quality if you can use that, which avoids any digital>analog>digital conversion and the small amount of associated delay (which is probably inconsequential for what you are doing), but the output from the RCAs should do you fine.