>you appear to assume that for calculations where "each mistake could cost $millions or lives", engineers who calculated by hand typically didn't double-check by redoing the calculation

Not at all! For any n extra checks, having an n+1 phase that takes a 20th of the effort is beneficial. I did include triple-checks to gesture at this.

>It is also unclear why multiplication and division have different difficulties, when dividing by n is equal to multiplying by 1/n.

This actually fascinates me. Computers and human both take longer to divide than to multiply (in computers, by roughly an order of magnitude!) I'm not really sure why this is in a fundamental information theory kind of way, but it being true in humans is sufficient to make my point.

To address your specific criticism: you haven't factored out the division there, you've just changed the numerator to 1. I'd much rather do 34/17 in my head than 34 * (1/17).