Thanks but DH has come up with a solution - we are propping up the loose-bottom of the regular 20cm tin (creating the shallow depth of tin needed) with a small loaf tin and hoping that the whole thing doesn't collapse in a heap. The whole thing is on a baking tray and seems stable - wish me luck!
I am about to make a three layer cake and have just realised I only have two sandwich tins of 20cm. I borrowed another one but it is 18cm. I do have a regular 20cm tin with high sides but I am a bit worried how a shallow cake will do in that. The mixture contains whipped egg white so I am a bit reluctant to cook two cakes and wait while they cook in case the whites slowly subside. What is the best option - three sponges of different sizes or two good cakes and one potentially rubbery one? I can't decide!