Quotes from CONF_iture:
"If you increase speed, you're not at alpha max any more."
That's only true if you maintain the same Nz. If you need to flare, you have to increase Nz (load factor) for the duration of the flare manoeuvre. As you know very well, Valpha-max rises with the load factor.
"If you maintain full back stick you maintain alpha max, therefore you maintain Valphamax - No speed increase."
That's only true after the flare manoeuvre has been completed, and the new FPA has been established. Then the Nz can return to (roughly) 1g. During the flare (i.e., the period when the FPA is increasing), the increased "g" causes an increase in Valpha-max. (See above.)
"What makes you climb in this case is a sufficient thrust increase alone."
The increase in thrust does help a bit with the flare, because of its vertcal component (at these high pitch attitudes). But its contribution is minor, as HN39 has explained
here.
"How would you want the pilot to go and get 'a small increase in pitch' as he's already full back stick in order to obtain and maintain alpha max ... ?"
If the EFCS does leave a small margin below alpha-max in 1g flight, as I am hypothesising, the quickest way to increase lift is to rotate the pitch and obtain (temporarily) a higher AoA.
This brings us back to your main problem - why was the published Flaps-3 alpha-max of 17.5 deg not achieved at Habsheim? I'm wondering if the EFCS only permits alpha-max when the a/c is in a turn, at a specific bank-angle/load-factor. If so, that might enable a sudden emergency turn without automatic de-rotation.