Independent and Moderate is not the same thing even though they often get conflated.
Agreed. You have Angus King type Independents, and then you have Bernie Sanders type Independents.
Romney did very poorly among the moderate vote, and I'm sure the socon rhetoric from other members of the Republican Party helped create an unfavorable image, even though he did a decent job of toning it down. But as most have said, Romney lost because of his image as "an elitist, greedy businessman", not because he was too moderate or conservative.