Gentle correction? HA! We are sooooo tough here....
Sounds like you are on your way. The fact that the ammonia is dropping and the nitrites are rising means you are almost half way through the cycling period. This is one of the toughest times..... nitrite can be really toxic to the fish, and the bacteria that process it can often be subborn and persnickity getting going. But, hang in there, they really will! In time.
Until they do, you are going to have to work, every day, to keep the nitrites in the tank under control. Ideally, you want to keep them under 0.5ppm. If that means a water change every day, go for it. 10 gallons is really not much - you can do that in 10 minutes or so. Do not be afraid to change out as much water as you need to to get the nitrites down to about 0.25 at the end of the water changes - this will give you a bit of a cushion between water changes where the nitrite may rise to 0.5, but not higher.
I would also suggest getting a bottle of a product called Prime or Amquel+ if you can. This chemical will bind the toxic ammonia/nitrite from your water, still leaving it available for the beneficial bacteria to process. IT makes it non-toxic to the fish, yet does not stunt your developing cycle. It is GREAT stuff. Add it after each water change - and it can help hold the line on the nitrites until the next water change.
During the cycling of the tank, I would also suggest feeding LArry far far less food than you are presently doing. Less food in means less waste in the tank - less nitrites for you to have to deal with. Feed him lightly or every other day. IF he is a bit bigger - 3 inches and over, you can easily feed him every 3-4 days, very lightly, and he will be just fine. In fact, he will probably be the better for it, for his water will stay even cleaner.
When the tank is fully cycled, you can slowly increase his food, increasing the waste and the biocycle will grow to met the demands of the extra waste.
Water changes are Larry's best bet right now. And your cycle will grow and develop.