That's a good design, I like Roman Black's work but it's a constant voltage generator with current limiting, what you need is a constant current generator. The brightness of the LEDs is proportional to the current flowing through them but their Vf changes slightly with temperature and of course the battery voltage drops as it discharges. What you need is a device that drops a variable voltage in order to keep the load current constant, in other words, one that drops less as the battery voltage drops and allows it's output voltage to track Vf changes.
The classic method of generating constant current is to pass it through a fixed resistance so (Ohms Law) converts it to a voltage proportional to the current. The voltage across the resistor is then held constant by a feedback circuit. If the voltage across a fixed resistance is constant, so must the curent through it. This is what the circuit in post #3 does. The only possible improvement is to replace the linear pass element with a digital one but the circuitry quickly gets complicated. You might find help if you research "LED drivers" on manaufacturers data sheets (Maxim comes to mind), in particular the circuits for white LEDs although the color is irrelevant.
Brian.