Most of the references I can find use the mathematical definition of slope. A number of the definitions are ambiguous. After further search I found an article that seems to indicate American railroad practice uses the length along the slope and British uses the mathematical slope. I was not able to find an "official" definition in the U.S. context.
I added a comparison to my spreadsheet and found the two approaches yield the same result within 1% up to a 14% grade. (Example: A mathematical grade of 14% corresponds to an along-the-slope grade of 13.86%.) However, the grade calculated in Rich's diagram is the mathematical slope.
I do not see anything in the Mt. Washington description that would lock down which approach is used.
I guess everything in life is a can of worms. 
