From experience with other boards, the low power capability of the MCU is negated by power regulators and power LEDs etc.
This is correct. Arduinos are development boards/prototyping platforms and not specifically designed for low power applications. One common approach is to design a circuit specific to the application. The ATmega328P used in the Uno can easily achieve the 0.1µA specified in the datasheet. I don't have a Due, if I'm reading the right datasheet, the SAM3X8E can get down to 2.5µA. My gut is the ARM processor isn't targeted as strongly towards ultra low-power applications as the 8-bit MCUs, but I'm just talking through my hat. Still, if I didn't need the compute horsepower, I might tend towards an 8-bit device.
A year on a CR2032 may be stretching it, 2xAAA might even be a challenge depending on requirements, other circuitry involved, etc. Is "99.999%" the actual expected number? If it were me, I'd do my homework and make sure I had a very good estimate of the duty cycle.