don't sand into the material.
you need fist something to adhere to the melamine - surebond,esp or whatever it is called in yr neck of the woods;essentially tell the paintshop you want something
that will let you paint on ceramic tiles because it is much the same problem.
this esp stuff you wipe it on leave it for some time
wipe it off and then go for it.
so!
once you have established a transitional substrate
you can have some fun.
silicate based paints are soft to the eye and highly
alkaline and so resistant to mould and anti bacterial.
they are flat and wipeable.
you could use three close colours and one brush - just hassle them until you like the look.

cement paint is not the best option.
some limewashes like above...but somewhat dilute would look nice as well but probably wax finish over the top,
which will impart a glow and slightly darken the appearence.
cheers joe.