Some people have mentioned exercise bikes or walking. Remember, in the OP I already stated why those ideas wouldn't work.
Doing hand exercises with a stress ball wouldn't work either, as it's too mindless.
I've also seen suggestions for speed reading. I tried it once before, though I'll admit that it was self-taught from the Internet. I read books 1 and 2 of a 4-book story. I quit when I realized that I couldn't remember anything that I had just read. ("I took a speed reading course and read War and Peace in twenty minutes. It involves Russia." Woody Allen)
Somebody I know personally says she reads outdoors in the summer months where there's just enough activity going on around her that she can pay attention to reading and the environment. This sometimes works for me; however, the street I live on has too much activity going on, what with a park entrance next door and a convenience store just down the road a little ways. What it takes is some distraction, but not too much or too little. Another problem with this idea is it only works in the warmer months; right now it's too cold to sit outside. (The local library here in Greenfield isn't an option, as it's always too busy and distracting. It's too small and there's no quiet space to sit and read. At least they're aware of these problems and are trying to find solutions.)