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No it's not that simple, you can use 6870 parts. You just need the right junction box and battery
from http://carltonbale.com/shimano-di2-everything-you-need-to-know/ :
Synchronized Shifting and Bluetooth Wireless Units can be added to all
E-tube Ultegra and Dura-Ace systems but the battery has to be upgraded
to the BT-DN110 Internal Battery or BM-DN100 External Battery Mount.
To add Bluetooth capability, a EW-WU101 or EW-WU111 inline transmitter
must be added to road bikes and for mountain bikes, the SC-MT800 or
SC-M9051 display/transmitter unit must be added.So @Shroom you can just about do anything, but it all depends on what parts you have and how fancy you want everything..
You could also use the di2 XT shifters (http://www.chainreactioncycles.com/nl/en/shimano-xt-di2-m8050-11-speed-shifter/rp-prod148576) instead of climbers switches.
Now onto the complicated bit, you prefer to use 2 buttons with 2 derailleurs, correct?
Shimano has something called "synchronised shifting" where you can setup the moment it switched chainrings through the PC software, but this needs a certain combination of junction box, battery or derailleurs. You can find out about it in their compatibility chart (http://e-tubeproject.shimano.com/pdf/en/HM-CC.3.2.0-01-EN.pdf). They are ordered by battery, then derailleur (scroll through it). It's not an easy thing finding the right parts for setting up synchronised shifting, so you could just go for the easy solution and mount 2 shifters.
Hope it helps :)