Would love some assistance on how to appropriately get a refund that I feel that I am entitled to.

Facts:
(1) Booked a ticket for travel. Realized within 5 minutes that I booked the ticket for the wrong dates. Called plat line to cancel the ticket. (the "Original Ticket")
(2) Explain to plat line agent that I booked for the wrong dates. Request cancellation. Agent tells me that she has cancelled the ticket.
(3) Agent offers to book me on the desired dates of travel. I tell her that I do not want to pay a fee to book with a live person, but she says that the fee will not apply.
(4) Agent tells me that the NEW ticket costs $X, which is less than the original ticket. I'm happy about this and express this to the agent. I give the Agent my CC and she issues me the ticket.
(5) Two weeks go by, and my refund has not been proceed. I call plat line today to get refund on Original Ticket. Plat line tells me that agent did not cancel the ticket, but only changed the dates, and that the $X charged to me was in addition to the cost of the Original Ticket, to account for difference in fares. Plat line apologizes for miscommunication, and declines to issue refund. Escalated to supervisor in SLC, who declines to issue refund. I take up the issue with @DeltaAssist, who is apologetic, but states cannot offer refund.

Note: the travel has already taken place. The original ticket was for travel the upcoming weekend. I had booked a Saturday/Tuesday ticket, when I had originally intended to book a Friday/Monday ticket.

Here is my problem. The agent on the plat line clearly told me that she had cancelled the Original Ticket. Agent proceeds to tell me that the cost of the new ticket is over $100 less than the Original Ticket. I'm not sure how else to escalate this issue, but I believe that I am entitled to a refund on the Original Ticket, based on the fact that I immediately called (ie, within the 24 hour cancellation policy) AND the Agent clearly told me that she had cancelled the Original Ticket.

Any thoughts?