They work offline because you downloaded the "binkwxx.dlls".
You applied both DLLs to the ">drive<:\Program Files (x86)\Origin Games\Mass Effect 3\Binaries\Win32" folder and did overwrite the existing DLL?
The save games however should work nevertheless unless they where created without a DLC that is now available again
(As the DLCs could not get registered.)
Lets try a different approche.
Then clear your Origin cache after the this guide:
All settings in Origin (only in Origin not in the games) are back to default settings after this.)