LDM ,
To keep the correct version short, the following is my summarized position:
Each time a ray impinges on an opposite fin (or any other surface), the radiant power is absorbed directly proportional to that surface emissivity (which is the absorptivity). The remainder is reflected or transmitted. In the case of alumina, the transmissivity is very limited, to less than 1 mm generally, and so can be ignored in the generalized case. That means the power directly proportional to the reciprocal of the surface emissivity is the reflected portion. If that remaining power-ray strikes another surface, it then imparts power again proportional to the absorptivity/emissivity and reflects the again the reciprocal portion, continuously dissipating the original power level until it is completely absorbed or goes to infinity and disappears from the system.
Total emissivity at the correct temperature is correct for the power absorption/reflection calculations.
This is the same as always, and results in no emissivity greater than one, or less than zero paradoxes.