What if... I am just thinking out loud here...
Fondant was my first thought, but only if it was thinnish & well adhered to the cake to prevent the weight of all those circles from bringing it down, making it stretch & sag? And good & dry. Then using a good adhesive. Maybe drying one row at a time? Just might work, too.
A thick fondant would fair better, be stiffer, but then no one would want to eat it, & it is a child's cake.
Buttercream might not fair much better. How were you going to 'adhere' them to the buttercream crumbcoat? Royal icing? More buttercream might just slip & slide around.
Have you considered a poured ganache of some sort as the base coat to adhere them to?
You can tell I'm an eager newbie, full of hot air... also not good for the icing on a cake. lol