From time to time, I find better ways of doing things, and the renaming thing is one of those. In my "mother" folders from which all offspring come, I rate images from 1- to 5-star. I am unlikely to look at the 1- or 2-star images again except in an emergency while the 3-star images might get upgraded by some random change of heart or change of use somewhere down the road. But I tag the 4- and 5-stars with appropriate keywords and tell stories about their importance in the Description/Caption field, which shows up in the Description field if I ever do Get Info in the Finder on my Mac. Another of those "better ways of doing things" is my new Rights Usage Terms, so every 4- or 5-star image is a candidate to get into the image collection on my website someday, so I'm re-saving every image so it has the new Rights Usage Terms in the metadata.
There are a number of cities where I've recently started naming the files based on neighborhoods instead of the cities because searching for a file that begins with "New York City" is like a needle in a haystack in my folder structure because I have a few thousand shots from there, as I do with London, Paris, Rome, and other cities in Europe and Charleston, New Orleans, Portland, and other cities in the US and towns as well, like Beaufort, South Carolina where I've shot enough for a small town that it helps to break the shots into neighborhoods. So in all places I'm now naming by neighborhood, I preface the filename with a short name for the city, such as NOLA, which is the locals' acronym for New Orleans, LA, as is NYC for New York City. In the Tweets and Presos folders (see OP) where the 4- and 5-stars go when complete, the preface keeps all images in the city together. This is especially helpful when two cities have neighborhoods of the same name, like Soho in London and SOHO in NYC, where the only difference is capitalization.
The problem is that there's a bunch of files saved by the old and the new naming conventions in the Tweets and Presos folders and I want to get rid of the old ones, leaving only the ones using the current naming system. What I discovered last night that's helpful, and which I added as a PS at the end of the OP, is that I can build a Mac Numbers database of all 2,800+ files in my Tweets folder (which should be identical to filenames in the Presos folder). What I learned since the PS last night might actually have solved my entire problem, so here's what I'm doing now: I went through the entire Numbers file and flagged all filenames that appeared to be from the old system with a yellow field background and all filenames appearing to be from the new system with a green field background so it's easier to locate them visually. I then created a column right beside the filename where a calculation delivers the last 4 characters of the filename, which is the shot serial number automatically created by my camera. So when sorting by serial number, it should put old- and new-system shots next to each other so I can flag the ones to check. But shots from other shoots might also end in 0040, for example, so I still had to tediously look at the date on each candidate shot to see whether or not to flag the old version. But it occurred to me this morning that I'm really rigorous about my file naming system, so the info right before the serial number in every normal filename is the date, expressed like this: 11MAY15, YMD format, so this is May 15 of 2011 so everything sorts mostly chronologically since the year is first and the day last. The only thing that gets mixed up is the month, since that's alphabetical. So it occurred to me that another calculation field that gets the last 12 characters gives me both date and serial (11MAY15-0040 in this case) making it really easy to see in a flash if I need to flag an old-system file for potential deletion.
So yeah, this is still a bit tedious but I can move really fast this way so unless someone comes up with a way of getting two windows into the same folder in Photo Mechanic Plus, I'm going with this... although the two-window capability would be great!
Actually, I'm adding this because the system described above may actually be superior for this reason: searching PM for date-and-serial as described above not only returns results from the normal Tweets and Presos folders, but also from backup folders on my Mac which I use because the normal Tweets and Presos folder are on a big external disk with which I don't travel. Searching PM also returns other files I might have named differently at some point. If it's a so-named file that's still useful for something like a blog post or a web page, I leave it where it is but it also picks up stuff I'm able to delete. So for now, it looks like this is the best way to work through this.