JBT, your quote does say "virtually no harmonics". I think it has to be something like pppp to produce only a pure sine wave in a resonating cone or tube. Audible pure sine waves sound very dull and lifeless precisely because they have no harmonics to enrich them.
I would have thought it was much more than mf when the reed starts to close completely against the mouthpiece. I know that change of tone but I don't think it is that sudden and I don't associate it with the reed closing, rather that you are hearing more of the whole sound including higher harmonics at louder volume (personally I don't like the term "beating" as it's usually associated with the intermodulation product, being a sum or difference, of two or more independent frequencies mixing, eg F1+F2=F3). I think the point at which the reed closes against the mouthpiece for part of the cycle is getting close to the point at which it stops oscillating - and hence producing sound - altogether.