Ultra low power audio recorder
You should consider ultra low power MCUs and audio codecs. 300mA is definitely way too much at 5V. Also if you can, and most of the MCUs and codecs can these days, reduce the system power supply voltage to 3.3V or less, say 2.7V or even 1.8V, unless you have a reason not to. Why 5V ?
Generally lower power MCUs are considered to be the MSP430s from Ti, and the AIC3204, again from Ti. You should be able to reduce from 300mA to less than 100mA if not more. Good luck.