Here's my take on your situation:
DO NOT ASK FOR SETTLEMENTS!
Get what cash you can out of your equity and pay off whatever it'll pay off. I think paying highest interest cards first is smart - but you may want to pay off the smaller ones first - strictly up to you. The CSR told you the right thing: Settlements will hurt your score! They will be closed and noted as settled for less than the amount owed. B-A-D!