This is not financial advice. I am not getting paid enough (or rather at all) for this and I am not a Bitcoin millionaire (yet). ;-) This is just an intellectual exercise. Thank you to @GuFinProf, Felicitas Opwis, and @JonathanACBrown for their support in this project.
Now, are cryptocurrencies halal? For those of you with no time who just want to skip ahead - the answer is: It depends. If you want to know what it depends on, keep on reading!