For some reason my reply has been deleted -- but quickly -- I managed to solve this issue by doing the following:
- Subscribed to iCloud (had not done that previously, even though transferring phone to phone always used to work fine!)
- Backed up my OLD phone completely (took about 2 days!) - photos, messages, everything.
- Restored my information from the cloud to the NEW phone from a clean install (wiped clean from previous attempts, at the "Hello" screen, choose from iCloud restore)
- At first, it did not appear to work -- but in about 12-24 hours, the "Photos" tab began to appear under the text message threads. I then had to open each one, click on it, and scroll all the way to the end, and this "forced" it to populate all the blank image slots and load them.
At times, this process would bog down, and it would just have an image of a placeholder gif, so I would have to shut down the NEW phone, restart it, open the iMessages app, go back to that thread, go back to the photos tab, scroll again to wherever it left off, and it would start populating the images again.
It took me a few hours, but it did finally work, and has worked since then for a few weeks now without incident.
This was a terrible issue, and I don't intend to keep using iCloud like this -- it was just for this one off and then I'll cancel and do the backup to my computer as I had done before and hopefully for the next update, this does not happen!