Does this topic help you out? It seems to be the same problem, and has a pretty detailed guide on how to fix the installation.
Yes it looks like StarJekker has isolated the issue and created a good workaround. I haven't tried to replicate the fault and use that method because my installation via the Origin client is working and recognized by the EA client now. I would if there was any debate about whether the fix works or not but I'm sure it does!
Thanks @Nyerguds for pointing us to that topic - I guess that is the correct board for this post too.
