That's quite literally multi-device >>sync<<, as in there is only one receiver and the rest is dependent on that.

Seems like a low effort solution and would not satisfy my requirements, but it probably works for some people.

I receive messages on my desktop regardless of whether my phone is connected to the internet or not.

Edit: just verified. Phone is in flight mode and chatting away on signal-desktop works just fine.

This is false. I've tested this possibility by turning off phone and Signal Desktop still receives messages. Description of plan around which protocol was build is here [0].

[0]: https://gist.github.com/TheBlueMatt/d2fcfb78d29faca117f5

That's slightly better but still cumbersome to set up and with the primary device as a SPOF. What does the recovery procedure look like if you lose the master?

From what I've read in docs posted above, identity key is copied from S-Android to S-Desktop. If you lose S-Android, there are two possibilities.

1) Your keys are safe (device was encrypted and/or you've wiped it remotely, whatever). In such situation you could be able to transfer keys from S-Desktop to new mobile. AFAIK there is no such functionality yet (remember, its Beta).

2) Your keys are not safe. In such case no recovery is possible. Notify all contacts about the fact that they should "reset secure session", forgetting your Signal identity and establish new Signal identity.

Anyway, this is the only solution on market with secure chats and multi-device sync.

No, your claim is false. This has been claimed about Signal multiple times now on HN and I've never understood how people came to this conclusion, because it's just not true and never was. All your messages arrive on all your devices, even if all of them are off at the time the message is sent. It's stored in an end-to-end encrypted fashion on Signal's servers until you switch on one of them, at which point the message will be delivered. When you switch on another one, the messages will be present at that device as well. The only thing missing right now is the sync of old messages when you link a new device, but that's only relevant in the first couple of days/weeks of use.