Line a 9x5x2 inch loaf pan with a large sheet or two of plastic wrap so that the wrap overhangs the pan on all sides.
Put all the cream in a mixer using the whisk attachment. Whisk on medium to medium high for about 2-3 minutes. Stop just when peaks are forming - up to 3 minutes. .
Transfer half of the cream to a separate bowl. Add the rum to the cream in the mixer and whisk 30 seconds, just to combine.
Add the lime and lime zest to the other bowl of whipped cream and gently whisk by hand, just to combine.
Spread a layer of the rum cream on the bottom of the plastic-lined loaf pan. Spread with a spatula to cover the bottom. (about 1 cup).
Cover this layer with the cookies - breaking up as needed to create one complete layer. The pieces should touch - a solid, singer layer of cookies.
Spread a layer of the lime cream (about 1 cup) over the cookies. Then cover this layer with cookies.
Repeat this process, alternating whipped cream flavors until you end with a layer of whipped cream on top. It might be slightly higher than the pan.
Use the plastic wrap overhang to cover the cake. Refrigerate for 5-8 hours or overnight. .
To serve for a party, invert the cake onto a serving platter and sprinkle with lime zest. It's best to use a serrated knife to cut. To serve individual slices, lift the cake out of the pan, using the plastic wrap. Slice of the slices you want and then use the wrap to lift it back into the pan!
Leftover cake should be stored in the refrigerator and covered with plastic wrap. This cake can also be stored (after it has been setup in the refrigerator) in the freezer for up to a month. Defrost overnight in the refrigerator.