I hadn't seen his follow-up. Considering this is pretty old (original from 2015 and follow-up in 2016) there were not a lot of regulators in the market at that time
I'm going to try it with a step-up regulator from Aliexpress which I have. This is the one: HW 626 módulo de potencia de aumento de DC DC, 0,9 5V a 5V, 1,5 V, 1,8 V, 2,5 V, 3V, 3,3 V, 3,7 V, 4,2 V a 5V|Circuitos integrados| - AliExpress
With this regulator, I would need to use 4 rechargeable batteries (4.8v in total) and 2 dead batteries to try it out