How about getting info pass and trying to file at local office.
I got my EAD and my wife's AP from local office (even though the case was at CSC). My case got trnsferred later on (for some other reason). I think some local offices issues these docs even if the case is with service center.
As your case has already been transferred, they will issue AP for you, hopefully.
If I were in your place, I'll take filled app., photos and transfer letter to local office and try.
