There is an existing cocktail called a ‘Slow Comfortable Screw’, or, in its more advanced incarnation, a ‘A Long Slow Comfortable Screw Up against the Wall’.
This drink consists of Sloe Gin (hence the ‘slow’), Southern Comfort (hence the ‘comfortable’), Orange Juice (which is what makes a screwdriver a screwdriver and not merely a bloody big vodka; hence the ‘screw’), a float of Galliano (which is in a Harvey Wallbanger; hence the ‘up against the wall’), served in a long glass (hence… oh, work it out for yourself).