Thanks a lot.
Sorry I can't tell you more. I follow this area of law closely but am not qualified to advise anyone. Employment checks have increased significantly though, especially in STEM, so it pays to have your paperwork straight more than ever.
Don't procrastinate, you can get in real trouble if you do not observe the deadline requirements. Get legal advice, ASAP. Not on the internet, from a real person who specializes in that area of law. A consultation is well worth a few hundred bucks. Start here: http://www.ailalawyer.com/