When will the AA battery voltage drop?
I don't have good news for you.

Below is the discharge rate for Durcell batteries done by some company. Look at the DC label; this is a Duracell coppertop battery. The complete test can be found here: link.



There was no µA test (it would take too long), but I guess the voltage will drop below 1.5&nbsp;V after about 1-2% capacity discharge. There will also be battery self-discharge (very slow). My guess estimated time for 0.3 mA (300 µA) before dropping to 1.5&nbsp;V will be somewhere between 50-150 hours. You can test this; it's not that long.

I would suggest to use different kind of batteries. Alkaline and a 3.0&nbsp;V requirement is just the wrong battery for this application.

You can also consider different battery chemistry. If you use some lithium AA battery, for example Energizer L91 - they have much more energy "available" before voltage drop below 1.5 V, but be careful - they have also higher initial voltage (about 1.7 V) and they are expensive (in my country they cost 2-4x more than alkaline Energizer or Duracell).



Image from Energizer Ultimate Lithium L91 datasheet: link

However if you want to pull 0.3&nbsp;mA (300 µA) from battery for two years (over 17000 hours) - you need more than 5 Ah (5000 mAh) before the voltage drops below 1.5 V. This is probably too much for any AA battery available on the market.

There are also nickel-zinc AA batteries, they have nominal voltage 1.65 V, but they have less capacity (50% less than Energizer L91).

Another idea might be three batteries with a low-dropout linear regulator. Three AA batteries in series will provide more than 3.0 V until they are completely empty, but a linear regulator may be necessary for some devices - three new alkalines may have 4.95 V initially.