Dear Bob,
My colleague Ilaria would agree with you entirely that the real issue is theological, and so would I; but we tried to base our argument solely on philological method, because otherwise we would have been open to the charge of circular reasoning: we prove the meanings of the words from the theological position, and vice versa. I was the one who attempted to limit our evidence as narrowly as possible.
I believe you are right about the problem of different meanings in different contexts. Here, Ilaria and I probably have a slight disagreement. I would have said that aionios in relation to God refers to his role in the world to come, and that only by accident does it suggest “eternal,” since we know that God is eternal. We argued that aionios has two related senses: long-lasting, but also referring to the next aion; and many of the applications to God can be understood in the second sense. However, my solution too runs into problems, and you’ve put your finger on a major one.
All the best,
David