I incline to admit that your hypotheses works!

And a minor note about the "старее/старше" thing. I've never thought abouth this, your point is interesting.
However, I would say (other people might disagree) that "старше" is more like the comparative to "старший" (elder) rather than to "старый" (old).
And "старее" can be used referring to people in the sense of "even more elderly".

As to things, it's easy: старый is old, старее is older.
As to people, "старый" is not just "old". For example, the phrase "He is 20 years old" cannot be translated into Russian using the word "старый". How can someone who is just 20 be "old"? The adjective "старый" when applied to a person means that someone is in his declining years, usually after 70 or alike. In this sense, "старее" can be used as its comparative:
- Мой дед старый, ему 80 лет.
- А мой дед ещё старее, ему 90 лет. (Although, "старше" would also work perfectly here).

However, "старший" does not assume any specific age, it stands for one's relative age. So, it is fine to say "старший брат, старшая сестра" etc.
And its comparative form is "старше".
Антону 25 лет. Игорю 30 лет. => Игорь старше Антона.
Now, "старее" cannot be used, as none of them (Антон и Игорь) is "старый" (old). They are both "молодые" (young). But one is older than another. Here we can only use "старше".