Why don't you try making something that isn't a cake at all? I find that once you've replaced all the allergenic things in cake... Well its just a kind of pretty poor imitation of what it used to be! I think you can replace one, maybe two of those components well, but not three!
What about a beautiful jelly 'cake' with fresh fruit juices, and maybe even chunks of fruit in it. Get a beautiful jelly mould and make a big wobbly 'cake'.
Alternatively Malaysian/Singaporean kueh lapis is a delicious 'cake' of steamed non-gluten flours and coconut milk in a multitude of colours (and you don't need to use pandan flavouring, you can just leave it out). All the flours can usually be bought at your local Asian grocery store - here's a recipe http://kokken69.blogspot.com.au/2011/08/ra...r-kueh.html?m=1
I much prefer making things that are meant to be allergen free, rather than try to replace things and end up with a poor substitute.