Here's an attempt using medium lossy compression, 100 pixel size and every 3rd frame cut out:
Using either the lossy compression or color reduction only allows me to go so far before the animation gets too many artifacts & noise, unfortunately.
Here's another attempt to get a bigger image size under the file size limit by increasing the lossy compression and cutting out every other frame (I also slowed down the animation speed to try to make up for fewer frames)
..but I think I'm done playing with that for tonight, as I have work in the morning.