Sorry you're late enough to the party that it looks as if you've rushed your essay. There are semi-group approaches that try to capture the direction of time in QM, for example, but I think not successfully so far.
I suggest that something of the distinction between past and future can be captured, however, merely by distinguishing between raw data and statistics of that raw data, all of which is in the past, and models which generate probability densities, expected values, correlations, etc., which legitimately try to model both the past (which must be in some sort of conformity with the statistics we have) and the future (which gives predictions of what statistics will be). Thus, ideal probability models may be as if of a block world, while the less theoretical raw data and statistics are only of the past.
Another observation is that by not explicitly including in a model the environment with which an experiment interacts, even if only marginally, one immediately fails to predict the future (or past) evolution of the system perfectly. Hence however much a model may be a block-world, the real world is not the same. Maps and territory and all that.
I guess this is only to question the normativeness of your call for us to formulate high-theory models in a time-directed way. If someone can construct a model that captures the direction of time as a fundamental principle, I would be very interested to see how it works, but it does not seem to me to be an absolute need. Some of my current approach to this can be found implicitly in my essay, posted here October 27th, where I construct an algebra of observables to be invariant under time-reversal, expecting that a direction of time will be /contingently/ expressed by states over the algebra, if such a distinction is called for when modeling a particular experiment. However I suspect that my essay is tangential to my comment here.
You almost cry out that you wish "to thwart the possibility of `blockification'". If we make limited claims for the efficacy and beauty of our models, with a proper humility, not absolute claims that our models are precisely the way the world is, a blockworld structure of our current best theories does not have to be something from which great ethical or moral principles can be derived. But perhaps I have misread your commitment to the quotation above because of my own reaction to your strong wording?
Of course I think this is an interesting issue! I have tried to formulate the above POV in response to exchanges with other essayists. Thank you.
