The esp8266 is well copeing with low-power-consumption design.
All the ATtiny, mosfet, step-up etc looks like snakeoil to me.
Useing a LiIon rechargeable cell or a lithium battery will give you wekks (months) of operation.
If you go for the more expensive LiFePO4 rechargeable, you have a allmost perfect stable3.3V over ~90% of useable charge. Every modern chip is capable of handling the max. charge end voltage of 3.6V.
Monitor Vcc via read_vcc and do a final deep-sleep w/o wakeuptime if battery runs flat.
As easy as that!
P.S.: is you still think it's necessary to power off some sensors, just do it via gpio. If you are low on gpios, use an ESP-12, doesn't consume more than ESP-01