The semi popular Passover Haggadah by Rabbi Nathan Goldberg strangely puts drinking the fourth cup at the seder after starting a couple of songs from nirtzah.
I've never seen this in any other haggadah, and it seems wrong. The fourth cup was established to go with hallel, and it would make sense then to drink it at its conclusion, and not make an interruption with a couple of unrelated songs.
Is this a mistake? Is there some source for this "change"? Someone told me it's also like this in the Gra's haggadah, but I checked one version and that wasn't the case.