There is no chance that an appeal or court decision will tell USCIS to treat this case as if it were approved on November 2004. Zero. Nada.
If the "resident since" date was in 2006 or 2007, there is the possibility that USCIS could have approved it back then and failed to notify the OP. However, with GC date = filing date, and asylee backdating is not applicable, the GC date is obviously wrong and anybody will look like a fool trying to convince the court that the GC date should be used as the basis for naturalization eligibility. This is not the days of Ellis Island, when people were fully processed for LPR status in the same day.