It strikes me that you're overthinking this a bit. It's not (or it shouldn't be) all that complicated.
The two sentences describe the same factual situation. There is a person (彼) and his father is a teacher. What changes is the emphasis/framing of the sentence.
彼のお父さんは先生です is, at its heart, a statement about the father (i.e. the father is the topic). If you wanted to continue the thought, you might say, 彼のお父さんは先生ですから、教え子からの手紙がよく届きます。 "His father is a teacher, so he (i.e. the father) often receives letters from his students."
彼はお父さんが先生です, on the other hand, is a statement about 彼. If you continued the thought from here, you might get something like 彼はお父さんが先生ですから、子供の頃よく勉強させられました。 "His father is a teacher, so he (i.e. the son) was often made to study when he was a child."
Almost any sentence can be rephrased to topicalize a different aspect of it, as "topic" is not a strictly grammatical function like, for example, "direct object" or "subject" is. That's why both が and を can be replaced with は (or も, which similar to は does not dictate grammatical function) and only the focus/emphasis changes, not the grammatical role of the word being marked with the particle.