Update: I found this thread because I want to change the card on a ticket purchased last night (within the 24 hour cancellation period). First agent to pick up was willing to do it without any hesitation. As noted above, the agent had to create a new reservation, process the payment from the desired card and then cancel and refund the existing ticket. Was no problem as the same fare buckets were available. At one point as she was going step by step through the process she brought up that since this was a new booking the $25 phone fee would apply. However, she readily agreed with me as soon as I said it's not "really" a new booking and did whatever she needed to do to have the fee waived. In the end, it took about 15 minutes to accomplish after roughly 15 minutes waiting for a CSR. Note that new ticket and confirmation numbers will be issued.