Let me hopefully clarify some things for you.
The formation of the Biological filter ( the end product of the cycling process) is complete when you have the microbes that convert the ammonia into nitrites and the microbes that convert nitrite into nitrate. If you were to graph this process, it would look a Bactrian Camal ( the one with the 2 humps. ) When you start with no microbes you should have a test result of 0 for ammonia, nitrite and nitrate. Once you have an ammonia producer ( live fish, dead fish or an ammonia product) you will start to see the ammonia level rise ( the start of the first hump). Once you start producing enough microbes that convert ammonia into nitrite faster than the ammonia is being produced, this will be the apex ( top) of the first hump then you will see the ammonia level fall ( creating the other side of the hump) while the second hump ( the nitrite hump) will start to rise. This will continue to rise until the microbes that convert the nitrite into nitrates are abundant enough to convert the nitrites faster than they are being created by the first microbes and at that point, the Apex of the second hump, the nitrite level will start to fall creating the other side of the second hump and the nitrate level will start to rise. When you are completely cycled, it means there are enough microbes to convert all the ammonia and nitrites being produced into nitrate. So in a completed process on a graph, as the nitrate level rises, it will look like the neck of the camel with no head in front of the 2 humps.
Now, with all that said, the biological filter is a living breathing thing that grows and shrinks based on the level of ammonia present. You are correct that the absence of the continual ammonia has hampered your cycling.
So when you have a nitrate level as high as you do with a nitrite level as high as you do, you have to question the source of that nitrate. Nitrates that high should mean nitrites should be 0. Check your source water to confirm that there are no nitrates in it. If there are no nitrates in your source water, see if you can get a second nitrite test at a local shop to confirm your reading. IF your nitrite level is actually 0 and your ammonia level is 0 and your nitrate level is that high without it coming from your source water, your tank would be considered cycled but you would need to add a continual ammonia source to keep the tank cycled.

Do a water change to lower those nitrates then add in your stock. If your nitrite reading is accurate, you will need to continue adding ammonia until your nitrite level reaches 0 before your tank will be cycled.
Hopefully this helps.