A problem I have with all this is, how do we know what time means when we have quantum corrections like that? In the simple nonrelativistic quantum mechanics I am familiar with, time is simply a parameter of the theory, it is strictly a rule of thumb that this parameter will correspond to something we can physically measure. This "rule of thumb" is reflected in the formal structure in the fact that time is not an observable, does not have an operator associated with it, and even though it has an uncertainty relation with energy, it is not a conjugate observable to energy because all conjugate pairs are formally equivalent to momentum and distance. Maybe the situation changes in relativistic quantum mechanics or quantum field theory, but my impression was that these fixes don't completely resolve the issue.
My understanding of this is that you can formulate operators that function locally like our macroscopic time measurements, and they will be canonically conjugate to the energy operator, but there is no guarantee they will function globally like the time parameter. So this is the general problem I have, it seems to me the status of time in quantum mechanics is quite iffy-- we know how time works in our own experience, and we can make formal operators that behave like we measure time to behave, but we have no way of knowing if any of that would still hold true on the Planck scale. In short, we have no idea that anything we call the time parameter in quantum mechanics, and apply quantum corrections to and Bohmian trajectories ruled by, will actually function the way we imagine time should function in the early universe.
Put differently, it may not matter a whit if some t parameter can go to negative infinity or not, what we really want to know is if, in some sense, an "infinite amount of stuff can happen" looking backward toward the beginning. I'm not sure the quantum corrections resolve that basic issue, it may be just another essentially philosophically imposed assumption of the Bohmian approach that no formal theory can provide justification for. In other words, what if the t parameter in the Bohmian approach is nothing but a mathematical coordinate, that is locally tangent to what we regard as time, but does not retain that property on the Planck scale-- would that not make all this "the Big Bang never happened" stuff a tempest in a teacup?
Also, in regard to getting the scale of the cosmological constant, it seems to me it is circular reasoning. They embed the deBroglie wavelength corresponding to the length scale of the universe today, which is essentially the length scale when dark energy takes over the dynamics, and then pretend that this is some kind of "natural" parameter to place in their theory. If it is "natural" for dark energy to rule the dynamics starting now, then of course we are going to get a "natural" scale for dark energy, but the real problem is, it is not "natural" for dark energy to just start ruling the dynamics now! The current length scale of the universe is not a natural parameter to embed in any theory that claims to "explain" something.
Finally, let me add that this whole business reminds me of the expert debate on what happens inside the event horizon of a black hole. Without observational constraints on any of this, should we pay any attention to these guessing games?