Interesting. I think I can add a few clarifications.
Vang. Not if the sheet is already tight. We are also assuming the mast will not bend. Thus, the vang only pulls the clew down, like the sheet. What a vang does do is reduce twist on boats with short travelers.
Flattening reef. Only effective if the sail was cut with broad seam near the foot that provides draft. Many sails are flat in the lower sections and out haul is all they need, or can use. Sail-specific. Also a racer thing, as often the sails cannot be stretched past the band.
Cunningham. Mostly for attached-foot sails; loose footed sails can often simply be down hauled with less distortion. Also a racer thing, if the sail is already max dimension. However, a cunningham can help if the track is tight and the halyard tension is not distributed all the way to the foot. Otherwise, just crank halyard tension.
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Depowering is a whole nuther discussion.
We skipped rotating masts with prebend; as they rotate the draft in the middle is affected. Many catamarans. Reducing rotation flattens the sail, over rotation makes a bag.
Batten tension. If full length, ease the tension.
And as was stated, sometimes sails are blown out. Recutting can be fun.