Unless you have an over-riding regulation (Part 135 in the USA, for example), there is no requirement that the normal and emergency procedures sections of the flight manual be considered sacrosanct and incapable of being modified.
Most airliners don't carry the original flight manual on-board. They have the Flight Crew Operating Manual (FCOM) that references the flight manual sitting somewhere on a shelf. The flight manual has been modified for their operation.
Notice what it says at the top of the limitations section - these limits must be obeyed, or words to that effect. It does not say that at the top of the normal and emergency procedures section.
I used to work for Transport Canada doing engineering certification, including approving flight manuals, and it was never the intention to not allow people to change the flow of procedures in the flight manual.
Be prepared to justify your actions if the new changed procedures result in an accident or incident, but that's the way of all things.