The Puritans were a more radical branch of the Church of England, famous for their early role in the American colonies. "Puritanical," according to Wiktionary, has two meanings: one referring to things related to the aforementioned group, and the other to "Precise in observance of legal or religious requirements; strict; overscrupulous; rigid (often used by way of reproach or contempt)."[0]
Of course, one could argue that this is an adequate synonym for the word "devout." However, saying the Pope is devout is very different from saying the Pope is puritanical (and, given the word's history, somewhat ironic). It is technically correct, similar to your definition.
> The only bait-and-switch here would be if I sometimes pejoratively referred to policies as "politically incorrect" which did not in fact meet the definition I provided
Why would you pejoratively refer to something as "politically incorrect," if you think political correctness is bad?