McTage calls it "Carping's dirty little secret." I won't call it dirty, just damned effective.
To get that close you need a couple of things to line up for you. One, the fish needs to be in some cover (or feeding obliviously). Two, you need something to break up your silhouette. Three, you need the wind or waves to mask the sound of your approach. And four, you need to be a stealthy SOB.
Don't be afraid to bring your fly line inside the guides. Carp are generally lazy creatures. They like to be fed.
So dap that soft hackle right next to his mouth. I bet he eats it.
It might not be a tight loop and sixty foot cast, but you will store up some sweet visual memories. And you won't miss the take.