You might find this interesting. It won't generate 6V, however it will get more out of your batteries and provide more output current. It can take 5.5V max on its input.
The ST619LB is a step-up charge pump DC-DC converter which delivers a regulated 5 V ±4 % output at 30 mA and over temperature. The input voltage range is 2 V to 3.6 V (two battery cells).
EDIT: 8-Pin DIP: ST619LBN