We have redimensioned our data multiple times as we change from SCD2/SCD1 to SCD6 or found things wrong with one of the data streams, like you mention.
It's not too hard to remap your data, you just need to make before you truncate you data in your INIT step to clone it, (or clone within your time travel window) then you join your fact table to the old dimension on the old dimension key, and then join to you new dimension via the old dimension foreign key and time, now you know the old key to new key mapping. Now that becomes the source of your update, and if you do it one operate with all other ETL operations paused, you have maintained your data integrity.
If you cannot pause the live ETL processes, you will a multi step update where you have your new divisional table and old one live, and do your normal mapping to both, and fix your reads to coalesce the results, and then once your new facts are correctly mapping to new dimension, turn around and back-fill all the old facts with ND keys, and then you have no ND gaps, then you can stop the OD/ND coalesce, and then stop the OD mapping and drop the OD column...