Yes, we agree on that much.
No dispute.
Assumptions 1 and 2 are not explanations of why you do not believe in the Olympian gods. They simply carry the presupposition that no other gods exist. Basically, all you've done is to say that you chose to believe in a religion that excludes the existence of those gods. You could have picked some other religion that gratuitously excluded the existence of the Olympian gods AND yours. You know that very well. So you have indeed begged the question.
Logic only guarantees consistency of beliefs. Just because an argument is logical, that does not mean that its conclusion is true, only that it is consistent with the premises. In this case, your premises fail to give a satisfactory explanation of why you reject beliefs in Olympian gods on a priori grounds.
While he did not explicitly say that, he also did not explicitly say that you could assume the existence of your god. In fact, we both know that he did not intend the existence of your God to be a premise in your argument. If the Olympian gods existed, that would preclude the existence of your god, wouldn't it? Just apply modus tollens to your logical argument. To give an explanation of why you reject belief in the Greek gods, you must consider the possibility that they might exist. But you have begged the question by excluding that possibility from the beginning.