Your assay has shown the critical points of the hypothesis.
Here we would like to give the counterarguments.
1.Problems of the time thermodynamic time arrow.
After stable equilibrium of the closed system has been achieved, its quantum processes do not stop, but their directivity can be reoriented. We can assume that a peculiar matching of the conformal space - time takes place at a higher hierarchic level.
Certainly, it is not always evident. However, there are no absolutely closed systems: let a stable thermodynamic equilibrium be obtained in the thermostat; after that, a higher level process is brought to the forefront. If the system is left free, the thermostat casing together with all its content obtains the ambient air temperature with the lapse of time. On the other hand, we can artificially maintain the temperature of the equilibrium state; however, we will again use for this purpose external processes leading to the increase in the ambient entropy. In any case, in considering the further evolution of the system, we should expand its borders and take into account the hierarchy.
2.Evidently, macroscopic time of the quantum system is not deterministic.
To begin the statistic analysis, it may be necessary to take into account the effect of other microparticles that are important from the entropic process point of view. However, in this case it is not necessary to take into consideration all the microparticles constituting the measuring device. For example: if we use a potential well, we can consider the influence of all charged microparticles participating in its formation. I.e., the transition to standard electrodynamic characteristics is permitted.
Notice that the microparticle intrinsic local time is of the deterministic character.
For example: consider an idealized two-slit electron diffraction experiment. Let the diffraction grating be near the electron source, while the detector screen is far away. Assume that at the design moment the electron has passed the grating long ago and approaches the screen. If at this moment we close one of the slits, we will not obtain the diffraction pattern. It seems that the microparticle local time stops. Initial conditions and the measuring device specifications do not affect the result of the experiment.
3.I agree with you that there should be a more fundamental parameter. In fact we are talking about hidden-variable theory.
If we consider a microparticle within the period from a reduction to the next reduction and assume that its intrinsic time is stopped, we can assume also the existence of the microparticle intrinsic local space. Since in the previous experiment the electron has someway recognized that the slit is closed.
The opponents assert that it is not necessary to introduce the local complex space with rather strange properties. The wave function is a purely mathematical entity that can describe all the effects.
But just allow me to ask the community: what will occur if in this experiment we close the slit and open it again prior to the commencement of the collapse? The wave function won't change; and what about the local space? What was changed when we closed the slit? What were the changes under the condition that there is no time in the usual sense?