In the first paper:
It's funny how it is said that consciousness must be a property of matter. Through this assumption, they have made a false assumption that there are only two options to explain the integration.
Sure, this is the structure of the orthodox Copenhagen interpretation. A conscious choice on the part of the experimenter is required to orient the basis vectors to calculate the probability distributions. Attempts to eliminate this step creates the basis problem.
I don't get the logic behind saying that consciousness must be a property of matter. That consciousness is involved seems evident based on the fact that it was incorporated into the original Copenhagen interpretation, but it does not follow that it is a property of matter.
So here he is stating that he is assuming an objective collapse model, such as the GRW or Penrose Objective Reduction. The statement that it is "certain" that the collapse process takes a finite time is not correct. In the Copenhagen Interpretation one of the possible states is simply experienced.
But again, the original Copenhagen interpretation did allow for this. This was already done over 80 years ago, but now problems are created by then abandoning the original and experimentally confirmed model in favor of an objective collapse model. Now even with this model the EPR paradox is a problem. So it seems that in an attempt to avoid the subjective nature of the Copenhagen interpretation, and its involvement of the conscious choices of the experimenter, other interpretations such as these objective collapse models were created that now created new problems, and then consciousness is now then said to be involved, and is then trying to fit into the model that was trying to avoid consciousness!
Anyway, I know you are not defending this position, but it's fun to check it out, and to me it seems to be an incoherent way to attempt to explain consciousness. In order to explain consciousness in a materialistic way, it has to be said that matter has consciousness, and in order to avoid the problem of consciousness causing state vector collapse (because if matter has consciousness and consciousness causes collapse, then how can superpositions ever arise?), then you need to use some other interpretation of quantum theory such as objective collapse models, which then creates even more problems. Why not just use the orthodox von Neumann Interpretation that simply extends the interpretation of QM that is used in experimental particle physics?