I did separate undergrad degrees in Economics and Philosophy precisely because they speak to different questions.
Economics tell us what is possible; philosophy tells us which outcome we should choose.
I think you were closer to the mark when you said
At it's heart economics is both descriptive, prescriptive and normative
I would simply drop the normative part. Economics certainly attempts to describe the world, and in so doing it offers conclusions such as wedrifid's: to get X, do Y.
The lack of the normative part can be seen in e.g. Steve Levitt's finding that the availability of abortion caused a lagged decrease in crime. Is Levitt arguing that abortion should be more extensive? No--just describing the relationship.
In the same way, the actual science of economics doesn't say X is good, whether X is the natural rate of (un)employment, free trade, public goods, whatever. Individual economists certainly do espouse these positions, for a variety of reasons. The actual claims of the science, however, take the form "X will allow people to move higher on their individual value scales."
Whether these individual scales are "right" or even whether they are the only consideration in moral decision-making is the concern of philosophy, not economics.
The description you gave of economic theory completely ignores the origins of micro and macro economics, price theory and comparative economics.
The assumptions that underlie these disciplines are normative.
Steve Levitt's finding that the availability of abortion caused a lagged decrease in crime.
Actually that is descriptive statistics. Just as I pointed out before - economics without normative conclusions is statistics.
Doubtful, but in your undergrad you might have read one of the following:
Adam Smith's Theory of Moral Sentiments
John Maynerd Keynes' Ge...
Recently I argued that the economist's utility function and the ethicist's utility function are not the same. The nutshell argument is that they are created for different purposes - one is an attempt to describe the actions we actually take and the other is an attempt to summarize our true values (i.e., what we should do). I just ran across a somewhat older post over at Black Belt Bayesian arguing this very point. Excerpt: