The type of curds you're making with Milk Punch are high-temperature acid-set curds, which are going to produce a cheese similar to ricotta, farmer cheese, or paneer.
If you want to use it as soft farmer's cheese, the kind you'd put in blintzes (for example), then you don't really need to do anything. You could also use the cold curds in place of ricotta in recipes like ricotta pancakes. They would work less well in recipes that require the ricotta to be creamy.
If you want a firmer cheese, basically a paneer, then warm the curds somewhat -- 50C or so should do it -- drain them, and then hang and press them the way you would normal paneer.
None of this is any comment on what the flavor of the resulting cheese is likely to be. You've added quite a few spices, juices, and alcohol to the mix, and that will result in a pretty interesting cheese.