Oops, I meant to say "Byron". Sorry Byron!
Perhaps it could be the algae, I'm unsure. Do you have any live plants? If so, what kinds and how many? If you don't already, it would be wise that you a add large amount of some fast growing, floating plants for a few reasons- 1. They'll help lessen or obliterate the cycle issues by sucking up the Ammonia. 2. They'll help use up the Nitrates present in your tap water. (I've not heard of Nitrates being quite that high straight out of the tap. You have it rough that way! But it would be awesome for your plants!)
Also, if you have access to some substrate or filter media from a HEALTHY, established tank, you could "seed" your tank with that to give it a big boost in the cycle.
I'm not sure what to say about the API Ammonia test malfunctioning. After you add #1, do you invert the tube 5 times? After you add #2, do you invert the tube 5 times? Are you sure you're adding the correct number of drops (8) of each? Are you holding the bottle completely vertically as you add the drops? Are you reading your results in natural daylight? Are you waiting 5 minutes to read the results? Are you sure it really is reading inaccurately, and its not the other tests that are off? If you're doing it exactly correctly, I'm baffled as to why the test would malfunction. I've haven't heard of any problems with it when done correctly. I'm stumped!
Also, are you doing the daily 50% water changes?