Butter two 9-inch cake pans, then line the bottoms with rounds of parchment or wax paper. Preheat the oven to 350°.
Melt both chocolates together with the 6 tablespoons of water. Use either a double-boiler or a microwave. Stir until smooth, then set aside until room temperature.
In the bowl of an electric mixer, or by hand, beat the butter and 1 ¼ cup of the sugar until light and fluffy, about 5 minutes. Beat in the melted chocolate, then the egg yolks, one at a time.
Sift together the flour, baking powder, baking soda, and salt.
Mix in half of the dry ingredients into the creamed butter mixture, then the buttermilk and the vanilla extract, then the rest of the dry ingredients.
In a separate metal or glass bowl, beat the egg whites until they hold soft, droopy peaks. Beat in the ¼ cup of sugar until stiff.
Fold about one-third of the egg whites into the cake batter to lighten it, then fold in the remaining egg whites just until there's no trace of egg white visible.
Divide the batter into the 2 prepared cake pans, smooth the tops, and bake for about 45 minutes, until a toothpick inserted into the center comes out clean.
Cool cake layers completely.
While the cakes are baking and cooling, make the filling, syrup, and icing.
To make the filling:
Mix the cream, sugar, and egg yolks in a medium saucepan. Put the 3 ounces butter, salt, toasted coconut, and pecan pieces in a large bowl.
Heat the cream mixture and cook, stirring constantly (scraping the bottom as you stir) until the mixture begins to thicken and coats the spoon (an instant-read thermometer will read 170°.)
Pour the hot custard immediately into the pecan-coconut mixture and stir until the butter is melted. Cool completely.
To make the syrup:
In a small saucepan, heat the sugar and water until the sugar has melted. Remove from heat and stir in the dark rum.
To make the icing:
Place the 8 ounces of chopped chocolate in a bowl with the corn syrup and 1 ½ ounces of butter.
Heat the cream until it just begins to boil. Remove from heat and pour over the chocolate. Let stand one minute, then stir until smooth. Let sit until room temperature.
To assemble the cake:
Remove the cake layers from the pans and cut both cake layers in half horizontally, using a serrated bread knife.
Set the first cake layer on a cake plate. Brush well with syrup. Spread ¾ cup of the coconut filling over the cake layer, making sure to reach to the edges. Set another cake layer on top.
Repeat, using the syrup to brush each cake layer, then spreading ¾ cup of the coconut filling over each layer, including the top.
Ice the sides with the chocolate icing, then pipe a decorative border of chocolate icing around the top, encircling the coconut topping.
(It may seem like a lot of chocolate icing, but use it all. Trust me. You won't be sorry.)