JayB, great advice.
I exported (unmodified original) video out of Photos, but it converted the video from .mov to .m4v. Also, the test file was originally 80MB and the exported version is only 25MB. When I re-import the 25MB version, it plays on all of my devices perfectly.
However, it loses all of the meta-data (camera, date, time, location). Also, I'm concerned that there's a loss of quality as the size is only 25/80ths of the previous size. I tried looking in the Photo's Library files, but the masters folder is organized by the date that I imported, which makes it impossible to find. I was hoping I could pull the 80MB version out and then re-import that.
Any suggestions or ideas?
UPDATE: I took the time to find the original and made a copy. Then, I imported it into Photos and it played on every device. Except, it's stripped of it's location and time zone data. I'm still not in a good position, but it's more data.