Hi, dr. meguro and SafetySteve, finally found the time to try the meguro-fix and - a miracle happened, it worked! Thanks a lot, ein großes Dankeschön!
After deleting the missing files, Photos properly transferred everything, no duplicates etc. I found appr. 100 missing originals (out of appr. 53000 photos, some years ago I had scanned almost all my old analogue slides and negatives). About half of the missing originals turned out to be duplicates (one normal file, one "missing").
Interestingly, almost all missing files were from Sept - Oct 2015.
And one more peculiarity: when now syncing I get a message, that certain video files cannot be transferred to the iPhone since they cannot be played on the iPhone. Moreover, the message indicates even the name of the file(s): 75F6DD40-B418-431B-86F7-F43A6684AC38.mov. Cryptical, isn't it? However, I cannot find such a file in my library, even not in the iPod Cache. At least for the time being, it is of no importance for me - as long as Photos simply skips this or these files and transfers everything else.
Photos offers also a repair function. I wonder a little bit why Photos does not - when repairing and in case of necessity - display a message of the kind "your library contains xxx files with missing originals which you should find or delet, otherwise synchronising may not function properly". This could be quite helpful. But - Ende gut, alles gut or all is well that ends well!