Im no expert but it sounds like Rekordbox is syncing ok but your problem may be the original file path.
If you move the file from the original path when you added it to Rekordbox then it wont play or move physically. It will still show as a file in your collection but its not on your drive as a file. If that makes any sense.
Not sure how you can see a waveform on the cdj and it not play though.
The files are on your pc but not in the original place when you added them to Rekordbox.
Thats why RB can't transfer them to ssd.
Hope that helps.