Do measurements of time-scales for decoherence disprove some versions of Copenhagen or MWI? Do measurements of time-scales for decoherence disprove some versions of Copenhagen or MWI?
Since these discussions of interpretations of quantum mechanics often shed more heat than light, I want to state some clear definitions.
standard qm = linearity; observables are self-adjoint operators; wavefunction evolves unitarily; complete sets of observables exist
MWI-lite = synonym for standard qm
MWI-heavy = standard qm plus various statements about worlds and branching
CI = standard qm plus an additional axiom describing a nonunitary collapse process associated with observation
Many people who have formulated or espoused MWI-heavy or CI seem to have made statements that branching or collapse would be an instantaneous process. (Everett and von Neumann seem to have subscribed to this.) In this case, MWI-heavy and CI would be vulnerable to falsification if it could be proved that the relevant process was not instantaneous.
Decoherence makes specific predictions about time scales. Are there experiments verifying predictions of the time-scale for decoherence that could be interpreted as falsifying MWI-heavy and CI (or at least some versions thereof)?
I'm open to well-reasoned answers that cite recent work and argue, e.g., that MWI-heavy and MWI-lite are the same except for irrelevant verbal connotations, or that processes like branching and collapse are inherently unobservable and therefore statements about their instantaneous nature are not empirically testable. It seems possible to me that the instantaneousness is:


*

*not empirically testable even in principle.

*untestable for all practical purposes (FAPP).

*testable, but only with technologies that date to ca. 1980 or later.
An example somewhat along these lines is an experiment by Lee at al. ("Generation of room-temperature entanglement in diamond with broadband pulses", can be found by googling) in which they put two macroscopic diamond crystals in an entangled state and then detected the entanglement (including phase) in 0.5 ps, which was shorter than the 7 ps decoherence time. This has been interpreted by Belli et al. as ruling out part of the parameter space for objective collapse models. If the coherence times were made longer (e.g., through the use of lower temperatures), then an experiment of this type could rule out the parameters of what is apparently the most popular viable version of this type of theory, GRW. Although this question isn't about objective collapse models, this is the same sort of general thing I'm interested in: using decoherence time-scales to rule out interpretations of quantum mechanics.
 A: I am not aware of any experimental evidence, so this probably does not qualify as an answer. However I can offer a reference that addresses this question theoretically:


*

*Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen (2011) Understanding quantum measurement from the solution of dynamical models, https://arxiv.org/abs/1107.2138
and by the same group, but more recently:


*

*A.E. Allahverdyan, R. Balian, T.M. Nieuwenhuizen. (2017) A sub-ensemble theory of ideal quantum measurement processes. Annals of Physics, 376C, Sciencedaily URL, full article: https://arxiv.org/abs/1303.7257
Essentially they do what the OP describes in the question. They take a dynamical model of a macroscopic system and solve its unitary evolution within the Schrödinger equation. Then they try to look if some "measurement-like structure" emerges just from the many-body dynamics, without collapse.
There is one main difference to decorence, where usually only a system and an environment is considered (e.g. the Leggett-Caldeira model, also cf. wiki article on quantum dissipation). In the work mentioned above, a macroscopic system that mimics a detector is included. Like the environment this is also a macroscopic system, but unlike the environment it has some special properties that allow it to record information. In the first paper this is done by considering a ferro-magnet, whose spontaneous symmetry breaking allows it to have a macroscopic polarization, which is essentially a deterministic property after equilibration (simply because the flip probability is very low).
As far as I am aware this is far from a solution to the measurement problem, some open issues are mentioned in the articles themselves. At least it goes into the right direction however, especially it starts addressing the question of measurement timescales, which can maybe also pave the way for experimental investigations thereof.
A: Do measurements of time-scales for decoherence disprove some versions of Copenhagen or MWI?
No. 
From Decoherence on wikipedia (emphasis mine):

Decoherence has been used to understand the collapse of the wavefunction in quantum mechanics. Decoherence does not generate actual wave function collapse. It only provides an explanation for the observation of wave function collapse, as the quantum nature of the system "leaks" into the environment. That is, components of the wavefunction are decoupled from a coherent system, and acquire phases from their immediate surroundings. A total superposition of the global or universal wavefunction still exists (and remains coherent at the global level), but its ultimate fate remains an interpretational issue. Specifically, decoherence does not attempt to explain the measurement problem. Rather, decoherence provides an explanation for the transition of the system to a mixture of states that seem to correspond to those states observers perceive.

As Wolpertinger said, to disprove Copenhagen or MWI you should challenge the postulate that the measurement act is instantaneous, by taking into account both detector and probe. I'm not an expert on this, so I cannot add much. I just wanted to point out that decoherence is not enough to solve the measurement problem.
Some further relevant quotes:

The discontinuous "wave function collapse" postulated in the Copenhagen interpretation to enable the theory to be related to the results of laboratory measurements cannot be understood as an aspect of the normal dynamics of quantum mechanics via the decoherence process. Decoherence is an important part of some modern refinements of the Copenhagen interpretation. Decoherence shows how a macroscopic system interacting with a lot of microscopic systems (e.g. collisions with air molecules or photons) moves from being in a pure quantum state—which in general will be a coherent superposition (see Schrödinger's cat)—to being in an incoherent improper mixture of these states. [...]
  However, decoherence by itself may not give a complete solution of the measurement problem, since all components of the wave function still exist in a global superposition, which is explicitly acknowledged in the many-worlds interpretation. All decoherence explains, in this view, is why these coherences are no longer available for inspection by local observers. To present a solution to the measurement problem in most interpretations of quantum mechanics, decoherence must be supplied with some nontrivial interpretational considerations [...]

A: Do MWI-Heavy theories require collapse to be instantaneous? I'm not an expert on foundations of QM, but intuitively I wouldn't think it's mandatory.
Isn't the essence of MWI the following: 
$(|0\rangle + |1\rangle )|\Psi \rangle\implies process \implies |0\rangle |\Psi_0 \rangle + |1\rangle |\Psi_1 \rangle$
For an observer, $|\Psi \rangle,$ making an observation is a process in which your observed outcomes are entangled with the state you wish to measure. After measurement, there's now an observer $|\Psi_0 \rangle$ measuring $|0 \rangle$ and an observer $|\Psi_1 \rangle$ measuring $|1 \rangle$. Checking which outcome you observe is equivalent to checking which universe you are in. 
The process of checking which universe you're in (verifying which observable you have) is an instantaneous process after the entanglement procedure, yes. But if wave-function collapse takes time, isn't this, in the MWI-heavy case, equivalent to having a time-dependent process entangling the observer with the state?
$(|0\rangle + |1\rangle )|\Psi \rangle\implies process(t) \implies |\alpha(t)\rangle |\Psi_0(t) \rangle + |\beta(t)\rangle |\Psi_1(t) \rangle$
Cutting the measurement process short (maybe by making a slow measurement, which then could be observed by interrupting with a fast measurement) would entangle the observer to states that are in some superposition of $|0\rangle$ and $|1\rangle$. So your fast measurement would then give you a distribution associated with this superposition state instead of the original state. This would give you some probabilistic information about which branch you have transitioned to in the slow measurement, but unless a full measurement is made it's simply a particular likelihood.
Doing some research it seems that the current debate on interpretations of QM involves a lot of discussion of the extended Wigner's friend thought experiment. Some think that the thought experiment shows that single-world theories cannot be consistent. Other's disagree.  But even those who think the measurement problem is still an open question believe that CI theories can be ruled out:

 It is clear that experiments that show increasingly large coherences
  can narrow the parameter regime in which spontaneous collapse theories
  might exist, but there is an enormous gap between current experiments
  and co- herence experiments on truly macroscopic objects...
  The Wigner’s-friend experiment can (in principle) discriminate
  between two competing quantum formalisms describing a measurement —
  the unitary relative-state formalism and the non-unitary measurement
  update rule. A specific combination of these two formalisms, together
  with the assumption regarding possible communication, gives a
  contradiction. We do, however, not regard a formalism to necessarily
  imply a particular interpretation like “many worlds” or “collapse.” We
  believe that the contradiction above does, therefore, not disqualify a
  particular interpretation of quantum mechanics. 

 So CI imposes restrictions that are falsifiable, while MW-heavy theories do not require this and, if anything, get stronger with such experiments.
EDIT: As said in the comments, there theories I'm referring to are not quantum mechanics with one axiom, but very specifically specify when collapse can happen. 
