Based on the work the person has done, if they wanted to make something with an exceedingly long battery life, and the battery setup there already seems to be basically a 1S li ion, they could graft in a back side battery holder for two high quality 18650 cells in parallel. It would probably last weeks.
A 10000mAh pouch battery would take up less room and provide more battery life. They are almost as cheap as 18650s too.