I think that you've argued the case quite well
galaxy flyer, no need to call for reinforcements!
757jetjockey, the author of those words included in your FCTM was a wise person indeed, I've had the pleasure of writing similar prohibitions in our own manuals.
Vmcg and Vmca are indeed predicated upon the Rated Thrust used. Even if a further thrust reduction occurs (as in the use of Assumed Temperature or Flex Thrust), Vmcg and Vmca are still based upon the Rated thrust used. This applies to derates, and similarly (in the reverse sense) to aircraft such as the Jungle Jet with APR OFF, and APR ARMED as Takeoff thrust choices.
Lower Vmcg in many cases leads to lower V1s, and everyone loves lower V1s. Lower V1 becomes particularly attractive when Wet or Contaminated runways are in use, because the appropriately lower Vmcg adds enormously to improved directional control (or JUST meets adequate directional control). Thus, increasing thrust beyond the derated Thrust at V1 may lead to serious directional control problems, or complete loss of directional control. In these circumstances, Reduced Thrust (Assumed Temp / Flex) COULD be increased to the Rated Thrust, but certainly NOT to Full Thrust Rating. My attitude to the latter point is to let "sleeping dogs lie", leave the thrust alone, and enjoy the improved directional control in the knowledge that sufficient performance exists in any case.
Similar arguments apply to V2, with the caveat that not a great number of takeoffs for long haul operations are V2/Vmca limited (because of the higher weights), but short haul operators who frequently use lower V2 speeds (because of the lower weights) governed by Vmca, may more frequently encounter Vmca limited V2 speeds. The problem is, when the engine failure occurs, do you have prior knowledge if your V1 or V2 is Vmc limited, and who does that? I don't, and I'm a performance nerd.
Thus, your operator has, in my opinion applied very sound policy.
During my performance nerding at my desk (not in the cockpit), I've found that the aircraft that I primarily handle for performance analysis is frequently V1/Vmcg limited, but the V2 speeds for all thrust ratings is the same. Thus I have incorporated into
THAT aircraft's operating manuals, "Following engine failure during Takeoff, thrust must NOT be increased to the full rating until V2 speed is achieved"
EXTREME WARNING - The above-mentioned allowance to increase to Full Thrust after V2 has been reached applies to this particular aircraft only. It may not apply to your aircraft.
In short, using a lower Thrust Rating is primarily beneficial for the continued Takeoff case, particularly on wet or slippery runways. Using the Full thrust rating is primarily beneficial for the Rejected Takeoff case (where Vmcg is not a problem for more than a second or two).
Conversly, for APR equipped aircraft (like the jungle jet), APR OFF is primarily beneficial for the Rejected Takeoff case, whilst APR ARMED is primarily beneficial for the Continued Takeoff case (unless the runway is wet or slippery). (A few other factors come into this argument).
Best Regards,
Old Smokey