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"
Interesting comment. While I agree with it, I wonder if many of the 'new generation' pilots understand it. I have not seen it so written in any ops manual of the 10 airlines I've worked for. But, indeed, there was 1 airline where the SOP on V1 cut was to increase to full power. Hm? Another left it to captain's discretion. Hm?
You say a/c type might be significant. B732, 733, 737, 739, B757, B767. I can't remember which of them was go to full power, but I hazard a guess it was a B767-300 operator becasue they didn't undertand the a/c in many other areas either. The Ops manual was written by an old B707 pilot.