Dear David Brown, I appreciate you for trying to include the neocartesian generalization of modern physics in your knowledge system and comparing it with the Lee Smolin loop quantum theory of gravity.
It should be noted here that in neocartesian physics, it is not length that is quantized, but the construction of the length by mass. The continuity of length arises from the Heisenberg inequality, which indicates that it is impossible to tear out a single point from space, since this requires an infinitely large momentum. So the principle of uncertainty passes into the principle of definiteness of points in space and makes them irrational points that complement the set of rational points to the continuum.
I wish you a deeper understanding of the neocartesian generalization of modern physics and apply your knowledge to deepen it.
Sincerely, Dzhechko Semenovich.