Wow. iOS is fussy about MPEG4 encoding. Stuff that worked fine as HTML5 video sources in Chrome and Safari on a Mac failed to load in various i-devices. In the end I re-encoded using FFMPEG and:

ffmpeg.exe"  -i input.mov -codec:v libx264 -profile:v main -preset slow -b:v 2000k -maxrate 400k -bufsize 800k -vf scale=-1:1080 -threads 0 -codec:a libvo_aacenc -b:a 192k output.mp4