That observation is very interesting, Mike.
I too find that I can actually operate either left or right dominant, depending on the prevailing situation, but I find it very difficult to swap over. The older I get, the harder it becomes.
If I am working, (using maths) I cannot paint. Literally cannot, the brain has no creative energy at all. If I start painting, I hardly function in the real world and really need a minder.
Once I was on a train and I was trying to come up with a logo and name for a client and the ticket inspector came along and stood beside me and I could just see his feet. I got really annoyed because I had no idea who he was or why anyone would want to disturb me. My daughter finally seized my purse and produced the required tickets. She wanted to know where I was!
When I am in creative mode, I cannot comprehend money or time or newspapers. Can't grocery shop, can't add up. It's very debilitating.
My flautist daughter, on the other hand, in her final year at high school, achieved the highest marks in the state for art, music and science. Of course, I think she is very well balanced. She measures up exactly in the middle, 9/10. I suppose she has well balanced genes.