Okay, I'll try it out.
But how do you post the video afterwards?
(Just to be clear, I don't want to set up any other accounts)
Just upload the .mp4 file to any video uploading website. Unfortunately, I don't have much experience with uploading content, but I'd assume YouTube would be pretty simple to get started on (well, assuming you already have a YouTube account, which, if you're already associated with Google, isn't an issue).
What you're looking for shouldn't be hard to find. I just Googled "mp4 to gif" and came up with a ton of results, like http://ezgif.com/video-to-gif, http://www.zamzar.com/convert/mp4-to-gif/, https://convertio.co/mp4-gif/, and more.