When making a film, most directors/producers aren't going to "waste" time and money in finding authentic music

They didn't need to "waste" time. As you pointed out, the Hardys did the ground work for them.

Given the time and effort that goes into get other aspects of period dramas right, surely it is not too much to ask that they get the music right as well. Hardy even gives them a start by mentioning tunes and hymns by name in the book.