Using Live Lead Pros for P&C

I am a relatively new health broker and I try to set appointments by calling aged leads. Half of the time they don't pick up or the phone is disconnected (these leads are anywhere from a few months to a few years old). But when I do get somebody to answer the phone, I tell them, "At one time it looks like you requested some information on affordable benefits. I'm simply following up to see what interest or need you may still have in that." Usually they say something along the lines of, "I already have health insurance". After which I am stumped, ask them a few questions, tell them that I could get them something better, and proceed to TRY and set the appointment with no luck (that is If they don't hang up on me). Basically I know that I should convey the message of "what I have to offer is better and more affordable", and then proceed to set the appointment. But being new, I lack the ability to structure a proper response which would get them interested in meeting with me.

So I would like to ask more seasoned agents, how do you go about overcoming that objection and turning it into an appointment. Any input would be greatly appreciated, so thanks in advance!