The 4th option does work. I know that because I sent my fafsa to 17 of the 20 schools I've applied to. USC was in the second group of schools that I sent to the FAFSA (the first "correction") and the USC site indicates that they received my FAFSA the same day that I did the secound round of corrections, which makes since because that was the day that I got the email back saying that my first corrections had been processed. Also, Wisconsin sent me an email (they were in the first batch, pre-corrections) that they received my FAFSA. I have no confirmation yet that those in the 3rd group/second corrections have gotten their ppwk yet, but since it worked the first and second time, there's no reason to assume that the third was problematic.
And doing the FAFSA and two rounds of corrections only took about a week -- so I don't know what this whole thing about taking weeks to get it all done is all about.