Mr O'Meara, a lot of folks have looked at this Altgens-Wiegman synchronisation question very closely. Mr Mark Tyler's outstanding 'Motorcade 63' animated reconstruction is well worth checking out!
https://www.marktyler.org/mc63.html

As astute as ever, Mr. Ford, no great surprise considering the credible source, who always seems to have an uncanny knack for sharing exemplary research. Appreciate the timely reference material within your shared link.
That said, it's also interesting how you honed right in on semantics. Again, no great surprise given that critical-thinkers like you aren't beholden to tunnel-vision. Your reference to semantics conjured up memories of my youth, where depending upon what region of the country my pappy was working in, the locals would make reference to , quote, " a soft drink, a soda, a pop and/or a tonic" when speaking of Pepsi, Coca-Cola, Dr. Pepper, RC Cola, Root Beer, Vernon Ginger-Ale, etc. So your point at semantics is a valid one. It wouldn't surprise if there are other items out there in our world that are also subject to a matter/manner of speaking depending upon the speaker.
Lastly, an excellent point at no one, and I mean no one has be able to credibly put anyone else in Prayer Man's specific position. They have nothing. That's very telling, especially more so given the revealing revelation in Mr. Hosty's notes. I'm open-minded enough to change my contention that Prayer Mn is in fact the wrongly accused IF someone produces a credible candidate to account for his position.
Any takers up to this challenge?