Export the images that you located in your search to the "moved_masters" folder rather than drag - copy. You can read more about how to do that here: How to export photos from Photoshop Lightroom
I don't see Export working for this. The objective is as much to get the files in the new location as it is to get the files out of the previous location. And to have LightRoom (LR) recognize the new location as the source for the masters. Export would get the files in the new location, but the files would also remain in the original location, too. And LR would still reference the original location for the masters.
Alternatively, I could move the files to a new temporary location, remove them from the LR catalog, and the re-import the photos into LR to moved_masters/year/month-day/. But I presume I'd loose any data stored in the LR catalog that's not contained in the image files. Another alternative, I could write a script outside of LightRoom to move the files as desired, but I think LR would loose references to the files and I'd need to re-associate inside LR manually for each file or folder.
Any other ideas?
When you move the images using the drag-n-drop in Lightroom, you are moving the images from where ever they were and dropping them into the one single folder you drag them to.
To maintain the original folder structure, you need to individually move the images from the old folder to the new folder using Lightroom, or do the individual file moves using Finder then doing a "find missing image" from inside Lightroom.
The only way to maintain the folder structure is to move the files one folder at a time where YOU maintain the folder structure. Under Windows, you can get the shell tools to create the empty folder tree for you. I don't know of the Mac has that option.
There have been numerous posts in the LR forum where user have lost files when moving a large number of images. If it's a small number of files ManiacJoe's drag & drop suggestion is the easiest solution. If you need to move a large number of image files in multiple subfolders I would suggest a using a different method as follows:
1) Backup your LR Catalog file and the entire folder tree structure containing the image files to be moved before doing anything. This allows you to recover and start over if something goes wrong.
2) Using Windows Explorer or Finder Copy (not Move) the entire folder tree structure containing the files to be moved in its entirety to the new drive location.
3) From inside LR select the entire folder tree structure containing the files to be moved and go to menu File> Export as Catalog.'
4) Using your original work catalog enter the same EXIF Filter terms. This will isolate the images you want to move. You will need to set menu Library> 'Show Photos in Subfolders.' Then Select All (CTRL +A) hit the Delete key and select 'Delete form Disk.' You have now removed the image files that are to be moved from the working catalog and from this disk location.
5) Next open the new Export Catalog file and use the same EXIF Filter terms, but with 'Don't Contain.' This isolates the image files that are NOT to be moved. Select All (CTRL +A) hit the Delete key and select Remove (not Delete from Disk). Note that the image files and folders that are to be moved will have a missing file & folders icon '!' because they no longer exist at the original location.
6) With the new Export Catalog still open reconnect the entire folder tree structure and image files at the new disk location as outlined here: How to find missing photos in Photoshop Lightroom
7) Lastly add the moved files & folders back into your original work catalog by merging the new Export Catalog file as outlined here: