Your screenshots do indicate otherwise, and I've not seen any cases of Lightroom losing a folder in the way you seem to describe. Anyway, go to the Library panel, All Photos, make sure you have all filters off (Cmd L), and then see if you can trace the image by the Filter Panel (set File Type to TIF) or by setting up a smart collection - eg looking for keywords contains Potosi, file type=TIF etc. That should narrow down whether it really is in the catalogue but has somehow got in twice. Also, optimize the catalogue - just in case it needs a kicking.
I don't know Spotlight well enough, but have you done a Cmd-F search where you specify things like last modified / opened dates?
I always do all my renaming and moving within LR, which is easier and doesn't require a synchronization, etc. I don't know why it appears that I renamed outside LR (or why that would cause the same folder to appear three times inside the catalog as you see from the screenshot), but I assure you, I didn't.
I did as you suggested, turned off all filters and used a smart folder to search my catalog (see screen shot); the images are easily found within the catalog using a number of different parameters. However, they won't open or edit (photo is "offline or missing") nor can I locate them on the actual disc when prompted to do so. Just to be clear here, ALL the images including the original DNGs are missing, not just the stitched TIFF (which was one of only two or three TIFFs in this group; most of the finished images in the folder were still DNGs) from this folder. I see no duplicate images, one working, one missing, or anything like that.
I went ahead and optimized my catalog, though I had just done this a few days ago (LR was crashing when using grad filter). No change, though.
I then ran a Cmnd F search and specified what exactly I was looking for on the disc. Should be fairly easy since I know the creation date for these files (see screen shot). As you can see, all the images listed as existing on the disc are .cr2 files, which are the backups I created when importing these images. The .DNG files (I always convert to DNG upon import, giving me DNG raws on one disc and CR2 backups on another drive) are not present in the search, though they were created on the same day as the CR2 files.