Design is largely about choices and options. To get anything done there will first be some baseline choices that narrow down the universe of options. Given an objective, some choices are obvious and others, especially the later more detailed, are not obvious at all. If the options suggested by the baseline choices turn out to be undesirable, it's time to change the baseline choices.
In this case the baseline choices are: using 2 Eneloop AAA batteries in series to power 3W worth of visible white light LEDs. The batteries are relatively well defined here, but explicitly, range is 1V < \$V_B\$ < 1.6V at 750mAh. Or, a source voltage range of 2V < \$V_S\$ < 3.2V. For the LEDs, just to keep things moving, figure use at 3V and 1A. We'll look at both of the input and output choices and see what kind of options these suggest. This will involve looking at source and load characteristics to decide what power topology will be most effective to use.
Input voltage less than 3.2V to supply ~3V says that a Flyback, SEPIC, or Boost (barely) would work.
Batteries like, as much as possible, constant current loads. So, to keep the input capacitance to a minimum (maybe zero), the Flyback is out, leaving the Boost (barely) or SEPIC. As an aside, should also leave out the output capacitor, since LEDs are current devices. This will also make any loop compensation a little easier.
Desire to operate the batteries down to the nubbin of 1.8V will mean minimizing conductive loss in the power circuit. That means no extra line length or switch to turn the thing on or off. So, the Boost is out since turning a Boost off requires an extra switch. SEPIC it is, since on/off function can be a micro switch to pull the chip enable down.
SEPIC
You would look for a SEPIC capable IC of either generic power supply or LED specific form. Preference goes to the LED specific form, because that will be minimal parts. The generic form would require adding a current sense amplifier. For more information about SEPICs this app note (slyt309) from TI is a good place to start.
Some numbers to narrow the search:
Duty Cycle (DC) at \$V_S\$ = 1.8V
DC = \$\frac{V_o}{V_o+V_S}\$ = \$\frac{\text{3V}}{\text{3V+1.8V}}\$ ~ 0.63
Inductor ripple current (coupled Inductor): \$\text{$\Delta $I}_L\$ = \$\frac{\text{DC } V_S}{2 L f_{\text{SW}}}\$ = \$\frac{\text{1.8V 0.63}}{\text{2(5uH)(500kHz)}}\$ = 0.225A
Peak switch current: \$I_{\text{Qpk}}\$ = \$I_o\$ \$\frac{1}{1-\text{DC}}\$ + \$\text{$\Delta $I}_L\$ = \$\frac{\text{1A}}{\text{1-0.63}}\$ + 0.225 ~ 2.9A
Look for a SEPIC capable LED controller that can operate down to 1.8V input with a peak switch current of 2.9A. These requirements are both on the margin. There are chips that will start at about ~2.3V and operate down to 1.8V. Also an external switch might be needed as ~3A on an internal switch is rare.
Here is a sample search for LED controllers at DigiKey. This is just an example of what search results would look like. Other suppliers like Farnell (Newark) or Mouser would give similar results.
No one, except maybe your next door neighbor will know what parts you can actually get where you live. It's up to you to find a part. If it turns out that you can't find a suitable part, it's time to change the starting point. Most simple would be to add a third battery to up the source voltage. A SEPIC would still be a good choice here.
If it turns out that you absolutely have to operate down to 1.8V and it is not possible to get an IC where you are that can do that, you might have to go to crazy options. As an example of crazy option there is this solar-cell light, a discrete circuit.
