When the sun reaches it's asymptotic giant branch star phase, it will certainly create carbon, but in general you're correct. Through most of its lifetime the sun can't generate anything close to a heavy nuclei.
However, I think you're on to something. At some point in the universe's development it became too big to scatter heavy nuclei everywhere we see them now. I think your approach could be used to set limits on when the heavy nuclei must have been created and what kind of stars must have created them.
The approach I was trying to suggest was to look at the stars in the early universe to determine how many heavy nuclei they could've created. Current ideas suggest that early stars were enormous. They should have been able to get close to producing heavy nuclei before going nova and scattering heavy nuclei all over the neighbor hood.
You're much better suited to make the calculations than I am since you've had some experience calculating cross-sections for fusion reactions.
Using this approach it might be possible to set limits on the size of the stars in the early universe, possibly to determine which came first, galaxies or central galactic black holes, maybe even set limits on the size of galactic black holes, and to set limits on the time when heavy nuclei would have had to be generated to create the distribution we see now.