I may gravely err due to misunderstanding, but, if the essential purpose is to enable a pair (and even a group) of communication partners (who know each other) to communicate entirely anonymously, then IMHO a email system of the following kind presumably should work well:
(A) Someone (hereafter designated provider) in a democratic country with comparatively liberal policy with respect to IT surveillance has the resources and the right to run a server.
(B) Ordinary mails by post from the users to the provider are not intercepted.
Mode of operation:
(a) Anyone can via an anonymous ordinary mail inform the provider a pseudonym and a corresponding password.
(b) The provider publishes on his webpage a list of the pseudonyms and the alloted serial numbers of the accounts.
(c) The user can have at any time a limited number (say 10) of posts of limited length (say 25 lines of 80 bytes) sent to him by his partner (who knows his password and who uses a neutral computer, e.g. one in an Internet-cafe) via an input window in the webpage of the provider and stored in his account in a FIFO manner.
(d) Anyone is free to view the content of any account via the account serial number or the pseudonym of the sender.
Some comments of my own:
(1) Concerning (B): A user from a highly non-democratic country may be able to let a friend living somewhere else to register for him.
(2) If the posts are well encrypted and with authentication (containing date and message serial number), even the provider couldn't do anything evil. For the worst case would be bogus posts, from which the communication partners would very soon learn of the defect. It
is of course assumed that the password system is ok such that no outsider can post into a foreign account.
(3) Possible financial problems for the provider could be solved via free donations from sponsors or users (including banknotes sent via ordinary mail) or allowing some commercial stuffs in the webpage of the provider.
(4) An attack through large amounts of bogus registrations is unlikely, for that is not done electronically but via ordinary mails, which costs something. I am not sure that server capacity exhaustion absolutely couldn't occur eventually but surmise that's in any case sufficiently satisfactorily solvable, e.g. through an expiration data of the accounts, raising a small amount of registration fees or yearly fees (with banknotes sent via ordinary mail), etc.
(5) Of course a provider with goodwill is assumed. Hopefully there would also be more than one such providers for any user to choose from.
(6) Mirror sites at different geographical locations may be considered in order to somewhat enhance the availability of the service in unexpected adverse situations. Surely the system would fail to function under the attack of an opponent who is mighty enough to break even certain fundamental security components of the Internet communication, in particular the digital signatures. (Nevertheless no secret will be lost, as long as the encryption done by the user is strong enough.)
(7) In the "degenerate" case, the provider may serve only a single group of anonymous communication partners and he himself may be a member of it.
(8) It is intuitively clear that the scheme described satisfactorily provides anonymity, unobservability, pseudonymity and unlinkability.