The reason why you want so much water is to protect the yeast. Eventually they'll produce too much alcohol and will start dying off. Try 2 cup sugars, 1/4 teaspoon of yeast, 1 tbls baking soda and fill the water up to the curved section of the bottle.
Before you try that, check your seals for leaks. Get lightly soaped water and spray or rub it on with a sponge. If it starts to bubble, you have a leak. You can seal it with silicone. Personally i don't use any adhesives to seal. I drill the hole smaller than the diameter of the silicone tube and force it through. That usually keeps it nice and sealed. This doens't work with co2 resistant tubing because it's too hard.