You are making it way to complicated…I don’t know why you exported and re-imported the FBX…
It is quite simple…
You have 2 files from UE, one the mesh and the other the animation…
Import your Mesh…select the armature…
Import your animation ( use same settings )
You now have two rigs on screen… delete the animation rig you just imported or hide it in the outliner …
Go to Dope sheet ( your mesh armature should be still selected if not make sure it is selected)
Change to the Action editor ( in the Dope sheet )
Go to the center drop-down and select the action that is in there…There should be only one, but in case there is more than that means that either your original mesh had animation data or the second import had more than one) if more than one…they will be named for armature 001 and 002 ( since you had two armature modifiers at one time)
Hit play…
I suggest if you still have problems that you share the FBX files from UE and I’ll see if there is something unusual about them…