On cooperation between left and right brains, I have experience in observing this relationship, having been a dancer. Teaching dancing heightened the interaction, because I would be doing one thing, telling my student, who stood facing me and doing the opposite, the opposite of what I myself was doing, and viewing the whole thing in a mirror.
This is a quadruple reinforcement of seeing, feeling and doing two things simultaneously.
Having to say the opposite of what you are doing, and doing the opposite of what you are seeing, can be mind-stretching. With a little practice it becomes second nature.
Dancing in general, as long as it is structured and deliberate, very much does what you propose with sight-reading of music, even more so, because it is whole-body operative.
In sight-reading, as with typing, there is some physical translation of visual input. Just reading text does it, too, because aside from the physiological component of absorbing the visual data, the brain has to translate it into conceptual meanings.
Where I disagree with your column on left-right dominance is your interpretation of which foot is dominant in, say, going up steps or stepping on a chair. As a dancer I can verify that it is not the moving foot but the supporting foot that is dominant! It holds and pushes.
And in my own case, I can report that I switch feet depending on which knee hurts more or less that day, so as to spare the bad leg the pain.
Having been trained for balanced function of both sides of the body through the dancing, I am able to switch without crisis reactions. I do it to this day because of the strenuous activity that my work requires.
You did get it right that when stepping off a chair, the moving foot is sub-dominant. The supporting leg controls the descent and must be stronger, working against gravity.
Those step exercises they sell on TV wisely make you use both legs alternately so as to develop both sides equally.
I can report on another two-brain activity. As part of my work, I have to interact with multiple people simultaneously. The necessity to do this was forced on me, and now I can do two different things together: speak and explain about products to one or more people, and write up a receipt for a customer, sometimes two receipts side by side for two different people.
No, I cannot write two different slips with two hands. Maybe I should start working on that stage of multiple dominances next!