Well, FWIW, I can easily write and count. It's actually way easier than I thought and takes no effort. Perhaps due to automatic touch typing while talking and thinking about something else etc? I can actually type and think about something else, never really noticed that before.
Reading and counting is harder for me. I can do it, but it's tiring. Those feel like they share lanes to me.
With touch type it would work if I buffer the work ahead of time and then I can type out the buffer while I count.
Sort of like: I think what I will type then when I start typing I start counting.
I do not generate what I type while I count, but think of it before I do it.