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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 :)
Uhm, planning on using some Di2 Climbers switch so I can use Di2 on some loop bars which means I will need to get some flat bar brake levers. Is this a stupid idea? If not, do I need to get two to control the front and rear derailleurs? Are there any other options available? I have 6870 for reference.