It is unlikely that ‘just’ fixing the problem with the SSA will fix it with the schools. I’m not sure how you got the FSA ID to work, but it sounds like you did so therefore your FAFSA processed. Now there is no method to get the FAFSA corrected from the SSA. The SSA doesn’t communicate with the schools.
Once the FA office gets an indication that there is a problem with the citizenship status, federal regulations REQUIRE the FA office to see the original document, passport or naturalization certificate. The school cannot release any federal aid without seeing the document. Some schools will accept a copy sent in to keep the process going but there must be a hold placed on the funds until that original is view at the schools FA office.
It’s really up to the schools whether they will process the FA and just put a hold on it or if they won’t process the aid at all without seeing the documents. You’ll have to work it out with each school.
Whatever you do, DON’T send the originals to the schools! Talk to them and explain that you know they can’t release the FA until they’ve seen the original docs, but could they please process the FA so you can see where you stand? Please? Please?