I ran into the same problem, luckily I had not deleted the files from the camera roll of my iPhone.
Photos.app will recognize the Live Photos as duplicates when already imported by Photo Stream as still photo.
The good thing is that you can reimport those "duplicate" Live Photos in Photos.app and they will not duplicate but will be replaced with the correct Live Photo version. Use "Import Selected" button.
The problem now is that manual selection of thousands of photos is not an option.... so I reimported the whole camera roll by dragging a frame over all the already imported files, including all duplicates (still photos and Live Photos) into the Photos.app. You will get an error message that "Duplicate bursts are not supported“, if you also have duplicate bursts to import, but that is even better in this situation avoiding unnecessary dupes. The rest of the duplicate still photos then can be filtered out using third party software like Duplicate Annihilator or PowerPhotos.
It is really stupid that the Photos.app is not giving an option to just replace the still versions of the Live Photos during import... would make our lives easier.
Don't forget to disable Photo Stream to not run into this issue again!
And make backups before messing around with your Photos.app Library!
I yesterday checked my iCloud settings on iPhone running iOS 12.2 and discovered, that somehow Photostream was active again. I am not sure how that happened. Had to go through the whole process again. I will now check after every iOS and macOS update if settings changed...