If you want an efficient way of serving chilled cocktails, just use “bottled” cocktails instead. Make the cocktail in the proportions you would normally use except substitute the ice for 25% water by volume of the finished drink. Put it inside a container and stash it inside your freezer until chilled. Then, you can either just keep the bottle on ice during the party or pour it into a thermos and serve from the thermos. You get the same taste as a well made traditional cocktail but for far less fuss.
I honestly don’t know why this technique isn’t far more well known. Sure, there’s a lot of theater involved in watching a well made cocktail being constructed but, apart from a few exceptions like the Ramos Gin Fizz which absolutely require a cocktail shaker to be made, bottled cocktails are going to be more consistent and far less stress to make while giving you a superior product.