Sorry for the incredibly late reply.
The idea behind the "soft consensus" is that in the end data equality *will* be achieved, because for a given transaction, one state will prevail over the other and be forever propagated by the network. The clashing transaction will eventually be rejected because of the opportunity cost of endlessly propagating a clashing transaction which is not likely to prevail (and therefore pays out no fees). Also, as a node operator, you can't just tack the clashing transaction onto every set of preimages you send out to the network ad infinitum in hopes that it will eventually be accepted, because then every state you send would be considered invalid, and all of your transactions in the set would be rejected. Users and node operators can try as hard as possible to propagate a given transaction by splitting the fees and paying other node operators to accept the preimage, but there is a limit to how far it can go.
One thing I didn't mention in my original post is that there are no miners per se. The nodes are the miners. But they are not mining in the usual sense - i.e. solving pointless mathematical problems to no end - however they are still expending energy and bandwidth trying to propagate the transaction preimages they have received in order for them to get paid out before other node operators.
Also, fundamentally there is no distinction between users or nodes either. Nodes are just users who are trying to make money out of propagating transactions. Probably they would have servers, fast internet, and their own algorithms to try to optimise extractable value.
The good thing about such a cryptocurrency is that it does not require any "core" software to interact with the network. The only "rule" that exists is what a preimage should look like, everything else is irrelevant. There is no block reward, no difficulty adjustment, no block size limit.... it all happens chaotically like water flowing downhill.
The overall purpose of this exercise is to try to imagine a cryptocurrency with as few arbitrary design decisions as possible.
Bitcoin and other cryptocurrencies are basically just hundreds of arbitrary decisions cobbled together into something that works. It works, so I can't be that critical of it, but I think we can do A LOT better if we rethink from first principles, and try to avoid arbitrary design features.