Here is a fairly standard charge equaliser, it costs around 10 US$ per unit.I'm only trying to help you.
Transistors are electronic switches. Two legs are like the in and out connections. When you apply a voltage to the third leg, it switches on. In the case of the balancing in that animation, the electonics detects that a cell has reached 4.25v, so it sends a voltage to the transistor on that channel. One side of the transistor is connected to ground and the other side is connected to a load (bleed) resistor. The other side of the resistor is connected to the top of the cell. That means that when the transistor is switched on, there's a path from the top of the cell through the resistor to ground.
The value of the resistor is normally around 100 ohms and it controls the rate at which charge bleeds to ground. Ohms law says thar the current will be 4.25/100, which is 45 miliamps. That's not very much. It would take 200 hours to drain a 9Ah cell group, which is why doing say one full charge in five isn't enough to balance your battery.
https://www.alibaba.com/product-detail/10S-18650-36V-48V-25A-Lithium_60839874905.html?spm=a2700.7724857.normalList.2.4acd4ffaOgctVl&s=p
You might even like this one better, it goes for around 18US$:-
https://www.alibaba.com/product-detail/16pcs-Universal-48v-Battery-Equalizer-Products_60764438912.html?spm=a2700.7724857.normalList.7.4acd4ffaOgctVl&s=p
None of the ones I have found online are nearly 400 UK Pounds......
But what you wrote is really not what happens with all the chargers I have seen.....
What do you think happens when the charger does NOT exceed the correct full charge voltage of 4.2 volts per cell?
According to what you say, it won't work, or do you now have a better idea.....?
You are apparently fixated on 4.25 volts per cell for some reason....
The web site I posted for you, you either haven't read it fully, or it went over your head.....
I thought that it was fairly simple and clear to understand!
I myself have been active in electronics since 1955!!!
Started with valves and very early transistors and RC control of aircraft and model boats! Went onto the RN and later 5 different major US computer companies.
You are going to struggle to show me how something works when you cannot even grasp the correct terminology!!
Especially as that web link did it so well, covering all eventualities.
This is your third attempt, I believe!!
Nothing you have posted works as you think it does either!
How sad.....
Andy