I recently had a schedule change that moved my flight by 9 hours and made the return flight impossible (I was returning same day, I only needed to be at destination for a few hours). Went through the process outlined above and of course it only offers me to rebook the day before or day after, which has same issue as original travel day. However, my original complete itinerary is available 3 days later and works for my schedule. Nope, told this is not possible. I do finally get an online agent who sees the logic in moving the flight and I was quite pleased to pay the $12 fare difference. Until I get the email confirmation - They charged me also the fee for booking online with a person, and added airport agent check-in to the reservation. And it charged my credit card on the reservation. So, contact again. I think the most blunt reply was "You will pay or you will not take the flight!" I ended up thankfully taking screen shots of the conversations (since apparently unlike any other airline you cannot save a log) and filed a chargeback on them with my credit card.
I'll fly Spirit and take the train an hour instead.