So I narrowed down the problem to two instances, both relating to "resetting" the data source. Obviously there are workaround, but it might be helpful for other users facing the same problem to come across a thread at least acknowledging and discussing it. Here are the instances:
(1) When trying to Set Data Source from ArcCatalog, some layers change their data sources, but some don't. Here's a quick demo:
The following replacements work
DF1: LYR11 C:\Users\Marcel\Documents\ArcGIS\places.gdb to C:\Users\mm1100\Documents\ArcGIS\places.gdb
DF1: LYR12 C:\Users\Marcel\Documents\ArcGIS\places.gdb to C:\Users\mm1100\Documents\ArcGIS\places.gdb
DF1: LYR13 C:\Users\Marcel\Documents\ArcGIS\places.gdb to C:\Users\mm1100\Documents\ArcGIS\places.gdb
...
The Following replacements don't
DF2: LYR21 C:\Users\Marcel\Documents\ArcGIS\Packages\db21.gdb to C:\Users\mm1100\Documents\ArcGIS\unified.gdb
DF2: LYR22 C:\Users\Marcel\Documents\ArcGIS\Packages\db22.gdb to C:\Users\mm1100\Documents\ArcGIS\unified.gdb
DF2: LYR23 C:\Users\Marcel\Documents\ArcGIS\Packages\db23.gdb to C:\Users\mm1100\Documents\ArcGIS\unified.gdb
(2) When trying to change the source by calling the replaceDataSource then saveAsCopy functions, the data source for every layer in every data frame does in fact change, but does not display because its corresponding attribute table is empty! When data is added manually by clicking Add Data and choosing the intended data, you get a duplicate layer in your data frame that actually displays, because its attribute table is not empty.
I hope my description highlights the problem now.