Also, brakes can be set so there is very little lever movement before the pads hit the rim, and so much space is left for hands. This can be difficult to get set up without rubbing as there will be little clearance for rim runout or flex.
Moving the levers in by about an inch should also help. You may also have to move the shift levers in, as they are usually inboard of the brake levers... this way, if the end of the lever gets closest to the bar at ~3 or 4 inches from the end, there should be plenty of room for your leftover digits.
And 'adjustable reach' for brake levers generally refers to the ability to be set closer to the bars for smaller hands. The don't get no bigger. But a few simple adjustments shoudl make it work better for you.