I have not read anywhere that you have to start classes in your current DLI. From what I can tell online and asking people already in Canada (including my intending DLI), you can change DLI on your CIC account once you have entered Canada and received your SP against your current DLI. If your new program requires a co-op permit that your former program did not, you can apply for the co-op permit once you have registered at your new school and started classes.
That's what I intend to do as well.