Thinking about it while looking at my hands (what a morning) I think different bars would help. Question is which bars. I think mine come in a 740mm / 12deg version so that seems like a logical start.
Actually I've found an out of focus pic. What you can see is that the shifter clamp can move in or out and rotate round the bar as much as you need. 780mm bars on this bike. Hardtail is 750.
Can't find one off-hand but I could take one later