I may be wrong, but from my point of view (E) is stronger than (A).
I agree that the word "both" forces us to take both parts of the assumption together. And I lean towards the second part as more compelling than the first one.
I think that the conclusion doesn't depend on: Drabble has no political debt that is of longer standing than the one she owes to Lee. Even if true, she is not forced to appoint Lee just because of that. Not even because is suitable. But because there is no other way to repay him, then most probably she will appoint him. I find this reason (E) to be the one that the conclusion depends on.
I think I found a way to "break" answer E.
Let's assume that answer E is correct and "The only way that Mayor Drabble can adequately repay her political debt to Lee is by appointing him to head the arts commission."
However, what if someone else (i.e. John) can only be paid with this position AND he is waiting longer than Lee for a repayment.
So, the question would be: Whom would get the job? Lee or John?
Since the argument clearly says that Drable pays her political debts as soon as possible, John would be the one to get the position.
Using this approach, I think we can put some doubts about the conclusion (Lee will get the position) even if we consider answer E as true. Therefore, E would not be the correct answer.
What do you think about this reasoning?
By the way, thanks for the interesting debate!