decoherence - Can the Montevideo interpretation of quantum mechanics do what it claims?

Partly inspired by the great responses to a my previous physics.SE question about "reversing gravitational decoherence, today I was rereading the intriguing papers by Gambini, Pullin, Porto, et al., about what they call the "Montevideo interpretation" of quantum mechanics. They've written lots of papers on this subject with partly-overlapping content; see here for a list.

The overall goal here is to try to identify, within the (more-or-less) known laws of physics, a source of decoherence that would be irreversible for fundamental physics reasons, rather than just staggeringly hard to reverse technologically. One can argue philosophically about whether anyone should care about that, whether such a decoherence source is either necessary or sufficient for "solving the measurement problem", etc. Here, though, I'm exclusively interested in the narrower issue of whether or not such a decoherence source exists.

Gambini et al.'s basic idea is easy to explain: quantum-gravity considerations (e.g., the Bekenstein bound) very plausibly put fundamental limits on the accuracy of clocks. So when performing a quantum interference experiment, we can't know exactly when to make the measurement---and of course, the energy eigenstates are constantly rotating around! So, for that reason alone (if no other!), we can think about any pure state we measure as "smeared out a little bit" into a mixed state, the off-diagonal entries in the density matrix a little bit less than maximal.

More precisely, Gambini et al. claim the following rough upper bound for the magnitudes of the off-diagonal elements. Here, T is the elapsed time between the beginning of the experiment and the measurement, T_planck is the Planck time, and E_A-E_B is the difference in energy between the two things being kept in superposition (so that $\frac{E_A - E_B}{\hbar}$ is the Bohr frequency).

(1) $\left| \rho_{offdiagonal} \right| \lt \exp \left( -\frac{2}{3} T_{planck}^{4/3}T^{2/3} \left( \frac{E_A - E_B}{\hbar} \right)^{2} \right).$

If E_A-E_B were equal to (say) the mass-energy of a few million protons, then (1) could certainly lead to observable effects over reasonable timescales (like a second).

Now, it might be that there's an error in Gambini et al.'s analysis or in my understanding of it, or that the analysis relies on such speculative assumptions that one can't really say one way or the other. If so, please let me know!

If none of the above holds, though, then my question is the following:

Can the bound (1) really do anything like the work that Gambini et al. claim for it---that is, of preventing "macroscopic interference" from ever being observed? More concretely, is it really true that anything we'd intuitively regard as a "macroscopic superposition" must have a large E_A-E_B value, and therefore a relative phase between the two components that rotates at unbelievable speed? In principle, why couldn't we prepare (say) a Schrödinger cat in an energy eigenstate, with the alive and dead components having the same energy (so that E_A-E_B=0)? Would such a state not constitute a counterexample to what Gambini et al. are trying to do?