Hi fishkur, same battery, same problem here. Did you find a solution?
I got busy and shelved this for a while but did try a couple things.
Like Vlad, I wanted to ditch the cells completely to eliminate hassles of overcharging, etc. I think it could be done but I'd probably recommend Diver's solution above (3 isolated chargers to handle each set of cells independently). This should satisfy safe charging though I'm not sure about the cell balancing. I see this as a way to extend the life a bit, not really a forever fix so my gut says each group of cells will be "close enough" to not bother with balancing.
Here's what I tried:
I ended up putting a DC/DC buck converter between the battery and a 12VDC power supply. I actually piggybacked some wires between the battery socket and the laptop pins just as a temporary test (before I got serious and started drilling holes in the laptop lol). This satisfied the clock/data/presence pins as they all remain intact and functional on the battery circuit board.
This is a video that put me on this direction:
The idea is that we need to control the current going into the battery but we are putting it in before the BMS (battery management system) within the battery itself. It will take care of load balancing, etc.
The buck converter pushes constant current (which you set) until the battery reaches a certain level of charge, then switches to constant voltage to maintain. You'll have to set the voltage to the pack (11.1V) and the current to whatever you desire. I'd recommend a low current which will take longer to charge but not stress anything since this is probably a bit risky.
I didn't get around to doing a battery calibration to figure out proper runtimes so my reported charge % and runtime would be all over the map. I did try running the laptop while charging and it worked fine, but wanted to do some testing with it under a full load and see if it would support this. Nothing got hot during the time I did run it...so potential win?
Ultimately, I accidentally yanked a wire out of the buck converter and caused a short circuit and blew up the IC...that happened this morning and I only stumbled on this because I'm retracing my steps to find the part that I ordered lol.
I will check back for the next couple weeks or so - if you (or anyone else) have any questions or comments I'd love to discuss.