I previously tried to do something similar—define an objective complexity upper bound by adding the complexity within a UTM to the complexity of the UTM. I don’t recall how I defined the complexity of a UTM—I don’t think it was recursive, though. Perhaps I used an average over all UTMs, weighted by the complexity of each UTM? But that still requires us to already have a definition of complexity for UTMs! (Unless there’s a unique fixed point in the assignment of complexity to UTMs, but then I’d suspect that function to be non-computable. And uniqueness doesn’t seem very likely anyway.)
I previously tried to do something similar—define an objective complexity upper bound by adding the complexity within a UTM to the complexity of the UTM. I don’t recall how I defined the complexity of a UTM—I don’t think it was recursive, though. Perhaps I used an average over all UTMs, weighted by the complexity of each UTM? But that still requires us to already have a definition of complexity for UTMs! (Unless there’s a unique fixed point in the assignment of complexity to UTMs, but then I’d suspect that function to be non-computable. And uniqueness doesn’t seem very likely anyway.)