Don't boil hops in water, boil them in a little DME, then add that to the keg. If you're worried about residual sweetness from the DME (since it's already too sweet) then add a little bit of yeast to it after it cools and let it ferment out, then add it. You should be able to add some bitterness with less than a quart of liquid and it should change the flavor too much. If you are really cautious you can use a small amount of specialty grains to mimic the stout. But don't boil hops in plain water, it doesn't taste right.
You might look at the hop shots available from NB too, I haven't used them and you still have to boil, but there will be less loss from the hop material. I don't know if those can be boiled in plain water.