Thank you very much for the suggestion. I just fear, the same problem occurs that way and the backup lasts a very long time. I do not think that this is Mac related. I remember that I had a similar problem a long time ago on a Windows machine.
I have now tried to repair the database and did some more researching.
1). There are other multiple named files and they imported correctly.
2). I deleted one of "not-importing" pictures and tried to reimport. No luck either
3). The one that does not import is actually a file that does not even have a duplicate in the (visible) database
I do not have the knowledge to answer your reconnecting issues. Maybe someone else can chime in with a suggestion.
Question: Are your pictures on an EHD? I don't think so, just checking.
Since I cannot come up with a solution other than to do a backup/restore I am afraid I can't be of much help. If you get this sorted out I would recommend putting the catalog and the pictures on an EHD and then you wouldn't have this problem in the future. You would be able to move the EHD from one computer to another.
Perhaps it is time to contact Adobe and see what they say.
When you took backup, did you choose to maintain Folder Tree hierarchy?
It is always advised to do reconnect before taking backup.
Anyways, once you restore (as many pictures as possible), import all images from your backup folder directly using File >> Get PHotos and Videos. Let's see if the duplicate (which are being left out upon restore) are imported or not.
Otherwise I would suggest a Full backup once again maintaining folder tree hierarchy, on your old machine and then restore on the new machine.