Apocalypse peaks in the "brand-new tune" line, I agree, but I would argue that it does not end there. There is a bit of postlude to it before the music moves on to As Sure As Eggs Is Eggs.
The bit between "brand-new tune" and "Can't you feel our souls ignite?" does not really fit to Apocalypse? But it doesn't really fit to Eggs, either! It's a transitional bit that's neither fish nor flesh (nor egg), but it's absolutely crucial to make the narrative of Supper's Ready come full circle.
During the first parts we have moved from the couple on the sofa through a succession of most peculiar images to nothing less than The End Of The World, the ultimate, final battle between good and evil - but before everything and the song dissolves in the eternal bliss of the New Jerusalem the scene flashes back ever so briefly to the couple on the sofa - and then the big cinemascope finale of heaven.
Should this transitional verse be assigned to Apocalypse? Or to Eggs? You could justify both. But as per the distribution of lyrics on the original Genesis have decided count it as part of Apocalypse. Artists' decision, and I can live with that. So, no, there's nothing wrong with Supper's Ready (apart from, depending on your recording and your point of view the facts that a) Peter sings it, or b) Phil sings it, or c) Ray has never fully sung it )
As an aside, with the record company's unblemished record of at least one stupid mistake per (re-)release it is also entirely possible that Genesis could have assigned the transitional verse to Eggs. But they have been consistent in this, which they usually have not been in their mistakes...