We love this cocktail in our house. The only issue is our ice dispenser makes crushed ice, but nothing like what you get in a cocktail bar so the "effect" of the creme de mure is not quite as effective, but still tastes great. I did consider using the food processor to blitz down the ice, but it wasn't entirely successful!
Perhaps invest in a Lewis Bag and Mallet for less than £20. The bag soaks up water so creating dry crushed ice. The more you wack the smalled the crushed ice.