I appreciate the attempt to hijack as the watermelon can be lots of fun. Of course my wife tells me I am too old for such adventures. I am also quite fascinated by the "pink panty pulldowns" and may have to have a party just to try those. I will go out on a limb and say this recepie can hold its own against those as the drink is much stronger than wine, but no one has any clue. The females seem to be particularly susceptible to the Sangria.
As for the cooler size, you are smarter than me if you did the math. If it fits in a five gallon cooler, there is no reason why you could not make it in such. We use the igloo water coolers because they have a spout. However, if your cooler has a drain, I do not see a reason why it could not serve as a spout. Also, You can use a ladle to serve. We sometimes have to resort to this even in the igloos as the fruit will clog the spout.
My only critical advice is to make sure you let it sit overnight. If not, the Brandy is definitely a shocking element.
. I think yours might be the trick. Drinkable with a kick.