You will need to fight for every minute of PTO, and if you call in sick it wont be on your first check. You will have to complain, and then they wont use sick time, they will use PTO and you will have to complain again.
The dispatch center is bad, and has no idea what is going on during the post shifts. Their only real job is to help manage the schedule, and they are bad at it.
They will hire people and pay them more than you, just to fill the schedule.