I feel like you've been sold a bill of goods, to be honest. Your results are exactly what one would expect an uncycled tank to look like. Actually what I think's happened is you've added too much ammonia and your cycle has stalled out.
The ammonium/ammonia thing isn't what your guy is making it out to be either. The relationship between ammonia and ammonium works as any other buffer does; they exist in an equilibrium where the relative balance is determined by the availability of the H+ ion. It's a mathematical relationship that looks like this when you graph it
Apologies for the lousy graph; I'm not exaclty a wizard with charts. Anyway it's got pH along the bottom from 0 to 14, and the percentage of the total ammonia that exists as either ammonium or ammonia along the side.
As you can see, at pH 7.4 you'd expect only 1.4% of the total ammonia to be in the form of NH3. So at 6 ppm total ammonia you'd have a NH3 concentration of 0.08 ppm, likely below the range of any hobbiest testing method, with the rest being ammonium. So your results of ~6 ppm ammonium and 0 ammonia are about what you'd expect.
Additionally, you wouldn't expect bacteria to convert NH3 to NH4+, because there's no energy to be gained in doing so (the reaction is spontaneous; any given molecule will flip back and forth between ammonium and ammonia instant to instant without any outside involvement).
I've had a read though this guy's stuff and a lot of it comes across as very reasonable sounding gibberish. A lot of the basic stuff he says is technically true; but he put it together into a discussion that makes it sound like he doesn't know what he's talking about. Speaking as someone with a certain amount of training in environmental chemistry, I can say he's sounds more like a clever advertiser hyping a rather ordinary product than someone making a science based discussion of a breakthrough innovation.