In a traditional analysis, absolute phrases don't have subjects.
The sun overhead and the sky clear, Carl stepped into his future.
Here, we have a compound absolute phrase. We have two coordinate phrases, each of which could serve as an absolute on its own, and the coordination as a whole serves the same function.
There is no clear relationship between this sun (or this sky) and either Carl or his future.
Instead of adjectives like "overhead" and "clear", your original example has nouns modified by participial phrases. Even if your framework requires you to regard those noun phrases as clauses with subjects, you still don't have a single subject, just as you would not have a single subject in a compound sentence. Phrases or clauses, there are two constituents acting in coordination.
He won his favorite competition, the long jump, and brought home another Gold medal for the United States.
He won his favorite competition, the long jump, and brought home the most fitting conclusion to his brilliant career in track and field.
There is a strong relationship between "another gold medal for the United States" and "the most fitting conclusion to his brilliant career in track and field". These two phrases have the same referent. They are different ways to express the same idea.
Two references standing together and sharing there referent are in apposition. The phrase in question in your second example is an appositive.