Imagine a pair of brake/gear shifters on a drop handlebar that look something like Campagnolo Ergos or the Shimano equivalent.
We are looking at the bar from the front.
Have a 'cable' loop that passes through both brake/levers. This could be a plain cable, or a chain, or beads on a string, whatever works best. I'll just use the term, cable, for convienience.
The levers only engage the cable when they are pressed inwards, otherwise they do not restrict its movement.
Pushing the right hand lever moves the cable loop clockwise. Pushing the left lever moves the cable anti-clockwise.
Mount a Rohloff gear changer on the stem, facing forwards, wrap the bottom part of the loop around the changer or have a cog that transmits the movement of the loop to the changer.
Pushing the right hand lever turns the changer in one direction, pushing the left lever turns it the other.
You could change gears without removing your hands from the brakes.
Don't get hung up on the whole wrap-cables-round-changers stuff, imagine that real engineers did a proper job on it.
Do you think that this could work, in principle?