I read through this book recently (and loved it). Without the benefit of a book discussion group--that would be so nice! What caught my attention in the discussion about piety was this idea: "piety signifies the duty, love, and respect owed to God, parents, and communal authorities." With that idea in mind, I don't think denominational differences have to matter. The fundamental point is that we, as persons (even small persons) have a duty toward others--toward parents first, then to other authorities (such as in a school), but also toward classmates. The duty toward God is very abstract, but it can be rooted in the small duties of neatness, orderliness, fair play, obedience, etc...that operate in a home and school.
I was reminded of Charlotte Mason's motto for her schools: "I am, I can, I ought, I will." That "ought" is that which is owed--the duties we owe to others, and even small children can begin to understand "ought" and their obligation to choose (will) to fulfill those duties. Line upon line, precept upon precept. I can see classroom practices such as being quiet while others are speaking, tidying your own space or belongings, lining up in an orderly fashion, puntuality, etc, laying a good foundation in piety, perhaps more easily (to be honest) than the happy organic chaos in a homeschool.
When I was reading the chapter on piety, though, I really appreciated the way these duties were linked to love, and helping children to learn to do things out of love and consideration for others is more important than just getting them done. "For inevitably, the culture of the school educates as much as its curriculum." Which reminded me of Charlotte Mason's principle "Education is an atmosphere."
I don't work in a school, but establishing that atmosphere right at the beginning of a child's school career seems like a good foundation in piety to me.