Basically, since BCS theory is only applicable to type I, how do I explain the occurrence of the Meissner effect in a type II?
you dont need to explain it, its way too complicated with vortex states, and how some parts act like normal conductors and others act like superconductors.
in fact, its because of this arrangement that allows for magnetic levitation that you observe in the classroom.
When you move it closer, it goes back to what it originally was, and when you move it further way, it goes back to what it originally was.
If it was a type I superconductor, it would just simply repel it until F(repulsion)=F(gravity)