For this recipe, the eggs are needed mainly as raising and binding agents, so you need a replacement that has more or less the same volume of liquid as the eggs would, and it needs to have good raising qualities. Possibly just throwing in a whole load of baking powder and water would work. I'd suggest some kind of water/arrowroot/baking powder hybrid, and you could use self-raising flour as well to be on the safe side. Then again you could end up with a monster cake that never stops growing like the porridge in that fairy tale but if you want this cake you have to be prepared to take risks. Or else just get some commercial egg replacer.