Dear Jonathan,
I'm happy to hear from you again.
You asked: "Foremost; does being able to address mathematical complications in solving Einstein's equations completely address Physics concerns near the Planck scale?"
My first efforts were directed to solving the problem of singularities in General Relativity. GR is about Einstein's equation, and not about Plank scale. The equations led to singularities, and my first concern was to see what happens there.
You said: "You are describing a unique construction where everything goes to zero ..."
It is not quite true that "everything goes to zero". Only some quantities go to zero, in a way which cancels what we expect to go to infinity. I tried to offer a mathematical description of what's going on there, and it appears that the things are better than it is usually claimed.
"... and the Planck scale is not conserved in any way, but the dimensionless point is rather tricky to correctly address even if you do make the event-horizon boundary go away, because going to 0-d is the ultimate dimensional reduction. Going there, even for a brief instant, establishes a condition where there is no metric as such."
I am not sure what you mean by conserving the Plank scale. Should General Relativity obey assumptions about a minimal length, which belong to other theories? I doubt. I can't see why the Plank length is considered minimal length, while we don't ask the Plank mass be the minimal mass. Obviously, the reason is that the elementary particles are lighter than that. Now, making the assumption that the Plank length is some kind of atom of distance belongs to some theories which consider that this will solve the problem of Quantum Gravity, and as a bonus, the problem of singularities, by forcing a bounce. But what if GR can handle its own mess? My point is that solving the singularities doesn't necessarily require modifications of GR, such as discretization of space, branes, etc.
While most of my papers on which this essay is based are about GR, a recent one suggested that singularities behave nice for QFT too, tempering the divergences in QFT and in Quantum Gravity. If this is true, then the main raison d'ĂȘtre of the discrete theories will vanish. I have nothing against them, but I don't think one should ask other approaches to copy them. Anyway, the approaches to Quantum Gravity try hard to mimic the successes of GR. Any success of GR will be inherited in the successful theory of quantum gravity, no matter how radical it may be. For this reason, even if GR will turn out to be a limit of a better theory (being it a discrete one), I can hope that my work will still be helpful, for the same reason why any advance in GR will be useful.
Best regards,
Cristi Stoica