What is the most controlled way to shift a red-orange sample toward red if it is too close to orange?

Correct answer: Add a very small amount of red

The governing principle is controlled colour mixing: to move a mixture toward one of its named components, add that component gradually. Red-orange already contains red and orange; adding a tiny amount of red increases the red influence and shifts the hue toward red. Yellow would push it toward orange, while green or blue could cool, darken, or dull the mixture rather than provide the most direct correction.