Unfortunately not possible, as the JSON is quite long. I've even gone the extra mile to calculate the average entropy of my game-state (its just numbers) to see how much I could save by compressing it, but to no avail. It would way too long, even compressed.
Thanks for the suggestion though!
i think it's possible.
this is an example: https://github.com/topaz/paste
in the big brain bucket, you could generate the url and use and url shortener