Well this is depressing, I just reimplemented the base64 URL to use LZ78 compression, but it turns out the input compresses so badly the URL only gets longer:
https://observablehq.com/d/87a3330fce4e42d3
I'm sorry, that sounds like a great idea though! I tried https://github.com/KilledByAPixel/JSONCrush the other day but it errored on first try so I didn't have a further look... But having shorter URLs would be great for sure!