Multi-cell li-ion charger
Your idea of grounding the step-down regulator to the cell it is charging is quite clever, but it won't work properly because its supply current also flows through all the cells below it. This will cause the lower 3 cells to get varying amounts of uncontrolled charge current that their associated chargers cannot get rid of, which will eventually cause them to become unbalanced and possibly overcharged (which is potentially very dangerous).   

To do it properly you need 4 fully isolated power supplies, or use a single 4 cell charger and wire a balancer onto the battery. Cheap 4 cell balancer boards are readily available on eBay and elsewhere. These often also have over-charge and over-discharge protection. 



If you use a protection board then the charger can just be a regulator with adjustable current and voltage, like this.

       

A charger built with these components may be more efficient, more reliable, and possibly even cheaper than a bunch of step-down regulators and TP4056 chargers.