Adafruit has a really nice battery charging/management breakout board that is small enough to fit inside a handheld. That way you can use a rechargeable lion battery to power it.I'm using one to provide battery back up to a wifi enabled freezer alarm. I get text messages if the freezer is warming up above 25 degrees, or if power is lost. (Wifi on APC) If goes above 32 a loud siren goes off and I get that alert as well. Saved my food a few times already because for whatever reason I have a hard time getting the door to fully close.adafruitOn board buck-boost to bring the 3,7v to a nice 5v
The nextion supply will probably be a deal breaker.. some of the back lights use 700ma alone..
How do you like the nextion display? I have two but have been too busy to do much with them yet.
Even a graphical lcd display would consume a lot less power.