The project prototype works reasonably well. The ESP wakes up every 5 mins to refresh the screen. It connects to the wifi hotspot, open a socket with the pilogger, refresh the screen and go to deep sleep. The hotspot connection process lasts around 5 seconds, event with fix IP. I should investigate to shorter that. However it stayed up for more than a week with a big 3200 mAh battery.

The prototype schematics looks like :

and the ugly wiring :

I ordered a more compact board on OSHPark:

https://oshpark.com/shared_projects/acNL1VCz