I've been converting the radar loops from GIF to MP4 files using Handbrake. It's free. You set the GIF file as the "Source" and then I use the preset "Social 25 MB 5 Minutes 360p60". Seems to take the largest GIF's and get them below my rather low attachment limit size. You can play around with the presets to see which one works best for what you want to post.
GIF's are very inefficient for showing motion graphics, they just happen to be an open standard that's been around forever, so if you don't have a file size to worry about they work, especially since it's easy to take one still image and make it a frame in a GIF.