Not sure what the problem might be. DCF is a file naming standard for digital cameras, so perhaps the TV expects file names that follow that format (e.g. a top level directory named DCIM, with a subdirectory consisting of a three digit number followed by five letters, with file names following a similar number/letter scheme; Wikipedia has a pretty good explanation of this). So if you're changing the directory and/or file names and structure, the TV probably won't be happy.
Photoshop does preserve EXIF data, but nothing in that should affect the ability to display the image itself.
Try this possible workaround:
1.— Take your original file (before any edits) and duplicate it.
2.— Work on the duplicate (exact clone) only. Do all your Photoshop edits to your heart's content. (Optional step: save the file, but don't close it so you don't compress the JPEG and deteriorate its quality.) Do a select all (Command+A on the Mac, Control+A on Windows) to select the entire pixel content of the duplicate, and COPY that. Now you have your edited image on your clipboard.
3.— Open the original file, and do a select all on it, but don't copy that! Instead, DELETE all the pixel content of the original. Now you have a blank image with only the metadata of the original.
4.— Paste the contents of your clipboard (the pixels of the edited clone) into the blank original. Save.
With any luck, you'll have the edited pixels with the metadata of the original.
It should work, but there are no guarantees.