That was covered in the article. Disrupting the default order allows you to put emphasis on certain words, in your case, you'd want the color adjective to stand out. The other option, which I don't think the article covered, would be to change the rhythm and speed of the phrase slightly and put an audible emphasis on red.

Yes rhythm and speed of reading matters too.

A writer and poet also has that in their toolbox.

If you're interested in the linguistic term, it's "prosody."

That is specifically addressed in the article.

As Partee points out, switching up the order of adjectives allows you to redistribute emphasis. (If you wish to buy the black small purse, not the gray one, for instance, you can communicate your priorities by placing color before size).

I found that example odd, as I would find it just as natural to emphasis the second adjective.

> No, the small black purse, not the small gray purse.

I read it as 'the Red "Big Barn"'.

red big barn is not wrong - it depends on emphasis.

Writers use these types of manipulations to change the meaning.