Good post, and I agree with your conclusion, but I'd try a different tack to get there - one that's probably the same argument encoded differently.

Instead of talking about "desires for the well-being of others" vs. "self-interested desires", I'd throw out the whole desire language and use the language of behaviorism here. Seeing others in pain is negatively reinforcing. Helping others is positively reinforcing. Therefore we help others.

Instead of the question "what desire is at the root of your helping behavior?" this suggests the question "why is helping others reinforcing?" to which the answer is probably evolutionary and has nothing to do with the character of the person in question.

If you then ask the altruist what desires motivated their action, they'll make something up, the same way people usually make up their reasons for stuff.

Also, am I understanding the experiment table right in saying that when subjects felt high empathy for Elaine, they were more willing to stay when escaping was easy than when it was difficult? Any ideas why that might be?