How to power a GSM Modem from a Li-Po battery?
In summary, you need to go from

Vin = 2.7 V to 4.23 V


to

Vout = 3.6 V  
Iout_peak = 2 A  
Iout_average = 500 mA.


If you use a big capacitor at the output, able to provide the 2 A peak without loosing too much voltage, you'll be able to use a buck-boost regulator that provides 500 mA average, at the output. For instance, the LTC3536 could work for you (which may deliver up to 1 A at 2.7 V input), and it's in stock.

Choose the output capacitor this way:

\$ C=\dfrac{I&#183;\Delta t}{\Delta V}=\dfrac{2&#183;0.0012}{\Delta V}\$,

where \$\Delta V\$ is the voltage drop you allow yourself to have, at that 3.6 V output. The smaller the drop you permit, the higher the capacitance you will need. For instance, to have a drop of only 0.2 V, you will need 12 mF (=12000 uF). Also, the capacitor must have a low ESR, to be able to deliver 2 A to the load.

Since the LTC3536 has an adjustable output voltage, you probably want to aim at a Vout slightly higher than 3.6 V, to compensate for the drop in the capacitor, or even at a clearly higher Vout, and use a 3.6 V LDO (but able to provide 2 A peak) between the big cap and the load, to completely hide the drop at that capacitor. That will allow you to use lower capacitances.