Dozy, is it your position that only the PNF was operating under the awareness that the aircraft was in Alternate Law? I do not think that what has been released from the CVR supports that position. As a number of others have noted, we have no access to various non-verbal communication that went on between them.
Further that point, given the difficulty PF had initially with roll control, one can be fairly certain that he was all too aware that he was in Alternate Law.
The more cogent point made is what BEA seems to have addressed in its findings of how and what preparation, training, and comfort with flying in Alternate Law at high altitude the crew had to fall back on. One could couple a "recency of training data point" to link to the choice to select TOGA ... which takes us back to Lyman.
If his mindset was overspeed, applying TOGA does not seem to fit the problem he was trying to solve.