With a un-balanced mic rig like this and access to both a soundboard feed, I'd run the SBD feed back to the stage (through the snake if available) and keep the recorder near the mics and battery box. Even if using a preamp with more ability to drive such a long cable run to the recorder instead of a batterybox (otherwise probably not necessary due to the high sound levels expected in the room) the long unbalanced run from the preamp back to the recorder would be suseptible to noise pickup.
One weakness of the DR2d is some potential for overload at high input signal levels. That shouldn't be a problem using low sensitivity mics powered with a battery box, and many of us have use the line-input on the DR2d for soundboard output recordings without problems, but on the outside chance that you do overload the recorder's inputs you can add some signal attenuators at the recorder's inputs to fix that.