The point remains that a Stirling cycle is quite
different from a Carnot cycle. It is not however
an "arbitrary" cycle.
a) Like a Carnot cycle, it is reversible.
b) Also like a Carnot cycle, it has a single
T(hot) and a single T(cold).
I think the preceding is the crux of the problem. Please explain in detail how you will accomplish a reversible isochoric process without a sequence of infinitesimally different temperature reservoirs.
So I think from an earlier message we do need to somehow average over each of these different temperature reservoirs in some clever fashion, perhaps tiling the Stirling cycle with a set of Carnot cycles?