Your list reflects my thinking almost exactly. The only thing I would add is make the employment verification system that is currently voluntary, mandatory. Don't know if anyone has responded yet, but I just saw something in the last two or three days regarding that program...I think one of the funding bills passed by both houses recently continues it. Problem is, I also believe it is still voluntary. It ought to be like NICS for gun sales...no approval, no gun. No approval, no job.
Yes there were several threads on the subject here's one:
http://www.freerepublic.com/focus/f-news/1025355/posts It is voluntary and has been expanded to all 50 states. We are already required to provide proof of identity and a social security card when hired into a new job. It makes sense to have a system to verify that the proofs offered are legitimate.