Great essay! What you point out is what happens at a singularity in RG flow, and the inability to continue beyond it means the solution on the other half could be something entirely different.
I have pondered the idea the Landau in gravity and QCD. Suppose SU(3) is really a reduction on SU(4) which as an STU type duality with SU(2,2). This is the isometry group of the AdS_5 and this set up is a form of gauge-gravity duality
Given a group G and a subgroup of it K to which it is spontaneously broken, the broken generators ("axials" in the chiral symmetry breaking paradigm of low energy QCD, SU(2)Ã--SU(2)/SU(2)_isospin is the coset space H=G/K. The generators of G than break up into the unbroken ones, k, (isospin), and the broken ones, hh, parameterized by the goldstone/pions serving as projective coordinates of that manifold (In QCD this is just S_3):
[h, h] ⊂ k,[h, k] ⊂ h,[k, k] ⊂ k.
The unbroken generators (isospin) close to a subalgebra, and the broken ones (axials) transform by the k as isomultiplets. In this way in the IR limit QCD recovers the isospin theory of nucleons.
So the idea would be that gravitation has a dual RG flow that hits a pole at the Planck or string scale. This would then lead to the emergence of new QFT-like physics or maybe forms of partons associated with gravitation. This might be one way the singular problems could be managed; we transform conformal gravity into a form of QCD where the IR limit there corresponds to the UV limit in gravity.
BTW I like you blog, though I have never commented there. I have been more of a lurker. If you have time you might be interested in my essay.
Cheers LC