I'm making a map that needs to run at the beginning of Portal 2, as it takes place just after Portal 1 and right before Portal 2. Is there a way I can package this change into a VPK, or something else?

People use the Developer's Console to play custom maps, I don't think it's a good idea to mess with the order that the official maps are placed.
When you release your map, you could mention in your description that it takes place in-between Portal 1 and 2.

Ok. I guess I'll just say that. Maybe I'll change it on my own copy.