I am not convinced that it's easy, or even really possible, to change from one thinking style to the other. Everything else I've read suggests this sort of cognitive leaning is largely innate.

I too think it's uncommon to completely change thinking styles, but I do believe it's possible to improve the weaker one. I also suspect one thinking style struggles more to develop the weaker thinking style, but don't know which one.

Do you have anything other than your own experience to suggest otherwise?

Being around many people who are into self-development, I often see logical thinkers being more intuitive and vice versa. No one makes a complete 180, but incremental improvements are common.

I am having some difficulty understand the "Ignoring your emotions" section, much less seeing the use of "fixing" this "failing"

The idea is that feeding emotional data to your intuition can help you better understand your own preferences, understand why you experience certain emotions, and how to illicit certain emotions in yourself and others. If you're not an emotional person, this is probably not a big concern.