I gave your question a try, with partial success. I read the abstracts on Cahill's homepage and picked out the one that appears to jump from quantum foam to gravity..Here is its location in cornell archive space:
gr-qc/0203015 [abs, ps, pdf, other] :
Title: Process Physics: From Quantum Foam to General Relativity
Authors: Reginald T. Cahill
Comments: 26 pages Latex, 1 separate eps file
In that paper on page 22 just before its end, he makes the following statement:
"In the absence of a derivation of the quantum-foam dynamics from the QHFT..."
So he admits not being able to derive the gravity terms.
QHFT stands for quantum homotopic field theory. This theory was set up earlier in the paper by assuming Schroedinger's equation applied to quantum foam. He talks about collapse of wave functions ad hoc, due to QSD terms that eventually become classical, so he says. He talks of qebits and Skyrmions, as emergeant characteristics of the foam. Sky.. are just solitons. He also says that self-referential noise is what makes the whole process go. Then he says without any demonstration that the process goes faster in the presence of matter and therefore the foam will flow towards matter.
That's when we get to the above quote. To get around that limitation, he assumes spherical symmetry and equates his formalism to Newton's theory of gravity. So at least in this paper he essentially leap-frogs the whole derivation by forcing his formalism to agree with Newton in the low speed 3-d symmetric case. Actually Einstein did the same thing in deriving GR, and DrDick did the same thing in his unified theory.
This approach works only if the formalism is rich enough to treat all of reality. Cahill was able to identify his non-symmetric term this way. But perhaps it is only the leading term in a more complete theory. Only time will tell. The same is true in all theories that have forced agreement with known theory in special limits. We no nothing of how complete the theory is.
So the next best thing is to compare the resulting ad hoc theory with experiments, and Cahill is in the process of doing that.
His approach has precedence. Feymann's QED renormalization is also ad hoc in that the infinities in the theory for electron charge and mass are arbitrarily replaced by their known values, which results in the most accurate theory ever as compared to experiments, even more accurate than measurements of charge and mass---it just amazing.