Thank you for all the great suggestions after the toddler + eggs incident! It eventually occurred to me, though, that given I needed to use otherwise wasted eggs, I could easily justify an experiment.
The last (and only) time I tried to make a sponge cake ended in disaster when I tried to remove it from the tin (visualise a large, deep handprint right in the middle of the cake and you get the idea...). So when this attempt made it successfully from the tin to the plate, we were already ahead!
The slicing and filling of the cake also worked!
While the tasting suggested that it might not win anything at the next Melbourne Show (a tad chewy - maybe left in the oven a minute too long?), it seemed to soften up over a few hours after being filled. I now think sponge cakes are not as scary as I thought, and I might start experimenting with some other recipes* and see how things progress!
Much creative excellence can be found at Kirsty's place, including some very cool giraffes from Pippiwillow, number 3 on the list!
* This one is Allan's Easy Sponge Cake from Everyday Cooking, the sequel to Everyday in the Kitchen, and very nearly as brilliant!