Same source, parallel charges for series batteries

Hello, it's my first post here so I hope I'm not breaking any rules.

I've ran into this problem while applying finishing touches to my project. I have 10S3P (or rather, 3P10S) pack of 18650 Li-ion batteries. I want to charge it using 5 of these (https://shdesigns.org/lionchg.shtml) simple charging circuits (since batteries are 3P, I replaced R1 with 0R5 resistor to double current output). I'll be charging each 2S3P "node" using separate charger, but the chargers in turn are powered from the same source. How do I avoid shorting Vout with GND between the chargers? Surely placing the diodes on charger Vout and between 2S3P "nodes" wouldn't cut it, right?

Also, since my budget for this work is now closed, switching to a completely different circuit design is not possible.

Thanks in advance for any help given.

A multi-cell lithium battery needs to have a balanced charger that prevents a weak cell from being charged higher than 4.20V and causing a nasty hot Lithium fire. If your 18650 cells have a protection circuit inside them and it is not fake then the very simple charger might be OK. A Chinese manufacturer sells a photo of a protection circuit that looks identical to a real circuit and it is installed on some fake batteries.