Your PA-to-DA calculations clearly differ from Cessna's, probably
because they used a different standard atmosphere. There are plenty
to choose from: International SA, U.S. SA, ICAO SA (all revised over
the years) and some others, some of which are no longer used. You'd
need to find out which SA was used by Cessna when the 172N was built.
Good luck with that project. I would just plot some points from the
POH and draw a smooth curve connecting them; I'd be conservative in my
choices of data points and call that good enough.