Cancelling health insurance through ACA Marketplace

Had my health insurance with Humana, through the Healthcare.gov marketplace. An agent helped me find new coverage outside the ACA marketplace and the new policy began as of June 1.

Called the customer service # on the back on my Humana insurance card to cancel the old policy. Humana tells me that they can't cancel it because it was a marketplace policy, so they transfer me over to the Healthcare.gov marketplace to cancel. They tell me cancellation won't be effective for 14 days, which will be June 22. So since my June payment to Humana had already been auto-drafted from my credit card last week, I'm basically screwed by paying for 2 policies for the majority of June.

My first thought was to call the credit card company and dispute the portion of the charges from today's date onward for their refusal to cancel the insurance on the date requested. But I don't know if they would be able to send me to collections and/or hurt my credit if I do that. Any advice or am I just screwed out of about $500?