I was constantly trying to book tickets at the BFI IMAX and ended up booking a Saturday showing at the Empire Leicester Square IMAX as a backup. Fortunately my brother was able to get through a couple of hours ago and managed to book a showing at the BFI IMAX. The midnight showing was full, but we got tickets for the next showing, at 03:15am. We both managed to get to the payment page using the Odeon app. Try it, if you haven't already. I can't tell you how relieved I am since I'm actually traveling to London from Greece.
As for Batman V Superman tickets. Of course they'll release them early. I actually just checked my e-mails for my booking confirmation for Man of Steel (I also saw that in London at the BFI IMAX) and the date was April 30th for a June 14th showing and I don't think I booked on the first day they went on sale.