No offense, but it seems like your confusion is arising from a desire to find something that just isn't there.
But a few observations:
Both the wiki and the New Advent site's only cite for the antiquity of the practice is the Life of St. Monica. However, I can't find any detail about the provenance of that Life. Late medieval Saints' lives are often less than reliable and full of anachronisms--in other words if the Life was composed at the time when 'cinctures' where first becoming a popular usage, it wouldn't be suprising if the author was projecting backwards based on a recent tradition.
However, even assuming that the Life is older/reliable, the description given is not of a common practice. It describes a private devotion undertaken by Saint Monica based on a private/personal revelation and then shared with a small group of friends. As such, one might compare it to something like St. John (of Shang-hai and San Francisco's) going barefoot. That's a private devotion with an extremely ancient pedigree (Moses and the Burning Bush) but not one that has ever been a *standard* practice. We know its origin and over the centuries certain Christians have been inspired to emulate it, but it has never been a formal or prescribed practice. If one wanted to start to go barefoot in emulation of St. John (or Moses) or to wear a cincture in emulation of St. Monica, I'd advise consultation with one's spiritual father, but otherwise it's purely a matter of personal devotion. There are no set standards or rules (obviously, in Late Medieval Roman Catholicism and afterwards there are but obviously you are looking for more than that).
Finally, if you follow the link in the New Advent site to their arcticle on 'cinctures' you'll find a different perspective on the origin. The actual cincture is not/was not a cord. It's a girdle (in the original sense of a thick belt). What is ancient about it is its use in ecclesiastical vestments where it has the origin of most vestments--that is, it was standard dress in Roman times; over time, secular fashion changed, but the clothes worn in Church by clergy remained static/conservative until the clothes item came to be seen as a strictly ecclesiatical item. And somewhere in the process, prayers were added to give the simple act of getting dressed a spiritual significance. Presumably, as the practice spread in the late Medieval West, laymen (and/or monks outside the Church) couldn't just start wearing what had become a formal vestment, but simplified it down to a 'cord'.