"(Only as those stars exploded did they forge heavier elements such as oxygen and spew them into the cosmos.)" I don't think this is correct - can't elements up to Iron be created through fusion in the stellar core?
Yes, but a lot of that occurs in the (relatively) brief phase near the end of the lives of very massive stars as their cores collapse. Once they run out of fuel for that process they explode in a Type II Supernova.