My math might be utterly wrong, but it looks like a Teensy in sleep mode consumes 0.23 milliamps at 3.3 volts, which comes out to 66 joules per day. The OP mentions that the mechanism provides about 13 millijoules per day, which is 5,000 times lower.
Teensy is nowhere close to most power efficient options out there. A power efficient arm can be running on micro or even nanoamps in sleep mode. It will of course depend on the rest of the circuit surrounding MCU.
