Sure. Here's what I have...Thank you for the reasoned reply. Since you have already done much research on the topic allow me to ask a related question: Do you know from whom or from when this "Freemasonry is a peculiar system..." saying originates? I do not, and the best I have been able to do in a quick search is to find references to it in the mid-19th century.
Sources
I: Other than “a Moral science”, how else is Masonry referred?
R: It is referred to as “a peculiar system of Morality veiled in allegory and illustrated by symbols."
I: When was it first referred to in this way?
R: Around 1813.
I: And who was first noted as making this reference.
R: Brother Samuel Hemming.
I: Who was he?
R: One of the leaders who helped unite the Antients and the Moderns into the United Grand Lodge of England in 1813 and one of its first Senor Grand Wardens.
I: What else?
R: He was Master of the Lodge of Reconciliation from 1813-1816, which he formed to bring about the union of the two groups.
I: What is he credited for?
R: He is credited with defining “Freemasonry” as “a beautiful system of Morality veiled in allegory and illustrated by symbols.”
I: What’s more?
R: He formed a new set of lectures known as the "Hemming Lectures," which was adopted after the Prestonian system was abandoned at that time.
I: What’s further?
R: Since its origin, Hemming’s phrase has been quoted in Rituals Worldwide; sometimes the word “peculiar” substitutes “beautiful,” depending upon the Jurisdiction Ritual used.
I: What Mason is known to using the word “peculiar” in this phrase?
R: Brother Albert Pike.
Privately Owned
I: What is peculiar?
R: Anything distinctive and differentiated from the usual or norm.
I: What’s more?
R: The Character of only one person, group or thing which distinguishes it from others.
I: What’s further?
R: Denoting special or particular qualities.
I: What is its root meaning?
R: Its root comes from Latin and means, “Privately Owned.”
I: How does this latter root meaning play into Masonry today?
R: Masonry is privately owned by the Body of Masons of each Jurisdiction.
I: What then is “Peculiar” to Masons?
R: Their Rituals, Lectures, Charges, Modes of Recognition, Character and Culture.
(FROM: Building Boaz: Uncommon Catechism for Uncommon Masonic Education -- Dr. John S. Nagy, second printing, pages 19-21)