Sulfur and its oxidized form are also needed by plants for proper growth. In fact your own body also needs it. Although you get all you need through Food. The macro nutrients plants need are nitrogen, phosphorous, potassium, sulfur, calcium, and magnesium. Another form of Ammonia that may be available to you is Ammonia carbonate.
https://en.wikipedia.org/wiki/Ammonium_carbonate
It was once commonly used as backing powder. Some people still prefer it. you might find it in grocery store or online.
I have not read of anyone using the carbonate or sulfate versions for fishes cycle. So I cannot say for sure that it will cycle an aquarium. Be advised that some ammonia test kits will not detect Ammonia chloride and i suspect that its the same for ammonia carbonate and ammonia sulfate. Since you cannot measure it in an aquarium you will have to weigh it. if you want about 0.003grams of ammonia sulfate or ammonia carbonate per liter of water in your tank. Your nitrite and nitrate tests should still work so you will know it is working when you see nitrite.
Adding a good plant fertilizer to your tank would also help because bacterial also need many of the nutrients in a good complete fertilizer such as Sezachen Flourish comprehensive.