i've got that part of the problem mostly covered. the cells will be severely de-rated, receiving a maximum charge voltage of 4.0v and a 200mA (C/10) maximum charge current. this will be backed with a small micro monitoring things and shutting down charging of individual cells when the charge current for that cell drops below 50% (100mA). even with these limitations, the design will still provide considerably better performance than the original lead-acid solution.
interestingly, there are few (if any) integrated parts that have any flexibility in reducing the maximum charge voltage. manufacturers tend to instead go for maximum stored energy and minimum charging time at the expense of cell service life. they also seem to prefer relying upon closely-matched cells welded together rather than using diodes (with the associated small voltage drop) to combine multiple strings of cells.
As a battery system engineer (too), I can say that series-then-parallel approach, is almost always the wrong one, and if you have to add diodes and special charging circuits it sounds pretty bad, and if you dynamically connect/disconnect cells/strings, then... $deity bless you.
Besides, I still completely fail to see how battery charging requires an anti-regulated supply with accurate-zero PSRR. If you roll your own, you still want a regulated supply, e.g 4.0V/cell, no?
This seems like a very classic X-Y problem, i.e. "hey guys I have this totally unorthodox and weird way of doing a normal thing and I think this is exactly what is needed, I just need a little bit help with X to make it work".
Just don't do it. Look for advice how to do it normally.