On the relation to decoherence, maybe "completely unrelated" is too strong but they say their model is "distinct from" and "not in the class of" environment-induced decoherence models. I think it's debatable if it is an "improvement" or not, but I don't think they get any closer to "solving" the measurement problem than Zurek does.

I find interesting that London and Bauer proposed a similar model already in 1939 (ref. [12] in the "Quantum mechanics of measurement" pre-print):

[9. Statistics of a System Composed of Two Subsystems]

"The state of a closed system, perhaps the entire universe, is completely determined for all time if it is known at a given instant. According to Schroedinger's equation, a pure case represented by a psi function remains always a pure case. One does not immediately see any occasion for the introduction of probabilities, and our statistics definitions might appear in the theory as a foreign structure

"We will see that that is not the case. It is true that the state of a closed system, once given pure, always remains pure. But let us study what happens when one puts into contact two systems, both originally in pure states, and afterwards separates them. [...]

"While the combined system I + II, which we suppose isolated from the rest of the world, is and remains in a pure state, we see that during the interaction systems I and II individually transform themselves from pure cases into mixtures.

"This is a rather strange result. In classical mechanics we are not astonished by the fact that a maximal knowledge of a composite system implies a maximal knowledge of all its parts. We see that this equivalence, which might have been considered trivial, does not take place in quantum mechanics. [...]

"The fact that the description we obtain for each of the two individual systems does not have the caracter of a pure case warns us that we are renouncing part of the knowledge contained in Psi(x,y) when we calculate probabilities for each of the two individuals separately. [...] This loss of knowledge expresses itself by the appearance of probabilities, now understood in the ordinary sense of the word, as expression of the fact that our knowledge about the combined system is not maximal."

[10. Reversible and Irreversible Evolution]

"I. Reversible or "causal" transformations. These take place when the system is isolated. [...]

"II. Irreversible transformations, which one might also call "acausal." These take place only when the system in question (I) makes physical contact with another system (II). The total system, comprising the two systems (I + II), again in this case undergoes a reversible transformation so long as the combined system I + II is isolated. But if we fix our attention on system I, this system will undergo an irreversible transformation. If it was in a pure state before the contact, it will ordinarily be transformed into a mixture. [...]

"We shall see specifically that measurement processes bring about an irreversible transformation of the state of the measured object [...] The transition from P to P' clearly cannot be represented by a unitary transformation. It is associated with an increase of the entropy from 0 to -k Sum_n |psi_n|^2 ln |psi_n|^2, which cannot come about by a unitary transformation."

[11. Measurement and Observation. The Act of Objectification]

"According to the preceding section, [the wave function after the measurement] represents a state of the combined system that has for each separate system, object and apparatus, the character of a mixture. [...] But of course quantum mechanics does not allow us to predict which value will actually be found in the measurement. The interaction with the apparatus does not put the object into a new pure state. Alone, it does not confer on the object a new wave function. [...]

"So far we have only coupled one apparatus with one object. But a coupling, even with a measuring device, is not yet a measurement. A measurement is achieved only when the position of the pointer has been observed. It is precisely this increase of knowledge, aquired by observation, that gives the observer the right to choose among the different components of the mixture predicted by the theory, to reject those which are not observed, and to attribute henceforth to the object a new wave function, that of the pure case which he has found."

They go on to discuss how "the observer establishes his own framework of objectivity and acquires a new piece of information about the object in question" while there is no change for us if we look at the "object + apparatus + observer" system from outside. The combined system will be in a pure state and we will have correlated mixtures for each subsystem.

London and Bauer say that the role played by consciousness of the observer is essential for the transition from the mixture to the pure case. Cerf and Adami claim to do without the intervention of consciousness but it's not clear how do they explain the transtion from the mixture to something else. They say things like the following, which doesn't look different from London and Bauer to me:

"The observer notices that the cat is either dead or alive, and thus the observer’s own state becomes classically correlated with that of the cat, although, in reality, the entire system (including the atom, the γ, the cat, and the observer) is in a pure entangled state."

From a very superficial look at the blog posts you linked to, I think I agree with some things (v.g. that most of this ideas have been around for quite some time), I disagree with others (v.g. that there is no measurement problem) but I guess most of the discussion is meta-physical so it cannot be "wrong".

I think dodging the measurement problem is not solving it. The core of the problem is here:

"But, while QM predicts that you will be classically correlated, it does NOT (and cannot) predict what the outcome of your measurements will actually be."

QM does not predict that the measurement will have an outcome. The transition from that probability distribution to one definite result is the measurement problem.