Hi there - I'm afraid there isn't a perfect solution to this and will likely be pros/cons to any approach taken.
For transformation rules, the only way to do Time dependent mapping is to use Composite rules e.g. T#2024M1:U1#ABC which is not practical in your situation because it would blow up the mapping and would need to include all time periods. This would also kill performance as composite mappings take significantly longer to process. For this, my only suggestion at the moment would be to create new data sources & import steps in the workflow and only use the new ones going forward.
Hierarchies are generally the best way to preserve historical structures so this would be my only suggestion although, comparing to previous data will need to be considered but can be accomplished via XFBR rules. You could also use text fields since those are time dependent to denote when members became active which could help with filtering member lists.
Again, not super easy solutions for this requirement. My suggestion would be to create a new scenario with the new dimensions assigned and reload all historical data there. They can still have the old scenario there for reference but it doesn't make much sense to have an apples to oranges comparisons across history when the mapping has changed.