As it turns out it was buried much, much deeper than that.
Yes, that is correct. Due to an abundance of stubbornness and an indomitable will I have "solved" it.
By "solved" I mean I got very, very lucky. Truly it was the nudges and prompts from the giants here upon which I am blessed to stand on their shoulders.
Giving it one last effort before walking away and setting up a completely new system using CertBot, I launched one final search. Rather than by name, I searched by time. If we did do the deed, there HAS to be a record. I was painstakingly combing through the search results, glassy-eyed and ready to give up when the anomaly popped up - a folder that I had not seen before, nor had it popped up on the searches based on the names of the ACME clients.
WACS.
What is a WACS? One waaaaaaaay too long Google-Fu session trying to get around the plethora of results for the Women's Army Corps of WWII, and all was revealed : Win. Acme. Also known by the moniker of WACS. Son of a...
I fired it up, and I found there is a log system of sorts. There it was - a perfect match of all the times the system jumped the tracks and successfully ran. It was a semi-automated system, in that it was screaming for help to an e-mail address that no longer existed and after many tries, restarted itself and started working again. It is why nothing appeared to match up to server restarts, et cetera.
For lack of a standardized naming convention, all was almost lost. That was why searching for Win Acme or Win-Acme netted nothing. There still isn't anything in the scheduler. There is no trace of anything at all if you do not know the keyword, so to speak. So someone here - in 2019 - set this ball rolling and good, bad or indifferent left behind zero documentation on it.
To paraphrase Adam Savage : the difference between science and screwing around is writin' it down. I will say it in the parlance of my dear ol' Comp Sci professor : Document. Everything. Way too many hours were needlessly wasted here because someone didn't take the time to document the trivial.
Thank you once again to one and all for helping me see the forest for the trees here. I do not have a clue to whom I should give the credit, so I will leave it to the collective wisdom of the brilliant people here. I would be more than happy to credit whomever you shove to the fore should they be bash-ful.
I am humbled, and still in awe of the sheer talent of everyone that chipped in so sincerely -
Thank you.