So here's a possible solution to both problems at once: I've always liked the idea of disincentivizing spam by charging a micropayment per email. So include a tiny bitcoin payment encoded into each layer of the doll to reward the intermediary, and you'll simultaneously provide an incentive for participation in the network (payment for participating) while simultaneously discouraging frivolous emails (since you now have to pay per spam message.) Obviously you'd make the charge small enough to not matter to most people for daily use (<$0.01) but I assume any nonzero price would hurt spammers badly.
You'd have to prevent intermediaries from decoding all the layers and taking the full payment, but presumably the Dark Mail folks have a solution for this already. Otherwise otherwise anyone in the middle could decrypt all the layers and read the contents of the email, and Dark Mail wouldn't work at all.
Or maybe I'm missing something. (Decent chance of that, since all I'm going on is a Time article and I'm not a security guru.)