1 mg/L ammonia is 0.0588 mM, so it will consume 0.0588 meq/L (= 2.94 ppm calcium carbonate equivalents).
So the initial assumption of 7 mg/L alkalinity per mg ammonia seems the problem.
Where did that come from?
Ok. It is a common number from water purification, but maybe it's just not the same thing...or maybe it's different in saltwater?? ...here are some random Google references:
http://www.weao.org/assets/docs/new-professionals/timconstantine-nitrification_and_removal.pdf (page 6)
http://waterfacts.net/Treatment/Activated_Sludge/Nitrification/nitrification.html (scroll halfway down the page to "Table 1: Oxygen Consumed During Nitrification")
http://www.environmentalleverage.com/Nitrification-balance.htm (third paragraph, just above "The Nitrification Process".)