Hi Chef,
this is the way grilled polenta has been always made in my family, and it works great.
As Pollyg said, make your polenta reasonably firm. Pour it, still hot, in a deep round bowl, level with a knife and cool it down. Refrigerate until cold. Unmold the polenta (you don't need to line the bottom with paper) and cut it, vertically, in slices of the required thickness. Cut your shapes out of the slices and they will be perfect. You'll have some leftovers, but considering the low cost of maize flour I don't think this is a problem...
Pongi