I gave up trying to get a deep navy blue fondant; now I just use the super blue luster to paint on fondant. Easier and tastier; and you don’t run the risk of making the fondant slack from adding so much color.
But, do you know the Whimsical Bakehouse cookbook? In it, Liv Hanson has a recipe for the “house buttercream” which the new owners inherited when they bought the bakery. Because it contains shortening as well as butter, it holds color well and they use this for all their “whimsical” cakes with neon colors. So you might be able to assemble and coat your cake with your usual buttercream (or a meringue buttercream) and then apply a final coat of the colored buttercream. It will still not be great, and you’re correct that it will stain teeth and tongues for anyone who gets one of those outside pieces of cake but it’s another option.
Personally I am not a fan of shortening in buttercream because of the taste, but it has it’s usefulness and color is one of them!