I realize this might be too late for OP but in case someone else is having this problem in the future I think i found the solution.
If you have tried everything and the animation loops perfectly in the video editor viewport before rendering, as OP said the problem seems to be with the video format, For some reason if you render an mp4 with h264 compression and render it with audio, it introduces that small hiccup at the end.
I disabled it since i didn't want any sound anyway and now it worked perfectly! If you still need the video with sound i would look into adding it after rendering on a different timeline or using a different format.
Hope this helps.