With a custom compression dictionary made against your JSON schema, I would bet you could still pack a surprising amount of data into 256 bytes that way.
I just used Pako.js which accepts a `{ dictionary: string }` option. Concat a bunch of common URL together, done.
The only downside (with both our approaches) is if you add substantially many new fields / common values later on, you need to update the dictionary, and then old URLs don't work, so you'd need some sort of versioning scheme and use the right dictionary for the right version.