I have no recommendations but I want to make a point. I am not sure if by 'communication' you mean speech or writing, but IMO writing is superior to speaking when you have to communicate ideas that result from analyses and critical thinking.
Such results often tend to be elaborate (or long winded depending on who is listening) and need the listener to participate actively. Unless you are an invited speaker tasked with dissecting a topic, no one is going to have patience, and courtesy, to allow you to finish what you have to say. If you are going to be doing that at company meetings, the interruptions will be worse. The person in the chair might even cut you short by asking you to get to the point in a passive aggressive way. One could argue that developing good speaking skill is all about conveying ideas succinctly, to avoid this very situation, but I differ. Your speech is only as effective as your audience allows it to be.
Writing, on the other hand, provides a better means to communicate such ideas. Firstly, your speech idiosyncrasies, like accent, pronunciation, voice etc, won't become an obstacle. Secondly, you don't demand the listener to be patient and attentive to what you say. The engagement mechanics are better. The reader can always reread a portion any number of times till they understand, or can take a break and revisit a portion if it gets a bit involved. Then, it provides a better means of recording exactly what your thoughts are, one that lasts for a time much longer than spoken words. This not only allows your thoughts to reach people farther down the timeline, it also serves as a snapshot of what your ideas and inclinations were at the time of writing. Retrospection (along with introspection) is a key factor in growing intellectually. Finally, it doesn't suffer from the Chinese Whispers Syndrome when disseminated.
Now, I don't mean you have to develop essay writing skills because not every argument needs an essay. While writing essays is a very good intellectual activity, a short and coherent paragraph or two suffices most times.
Critical thinking is very addictive. You might start off with something small, like why a club must have a player, or why a product design is not good, which might be communicated reasonably well via speech, but you will slowly get to bigger topics where what I wrote becomes applicable.