circuit looks to be hooked up correctly...

Does this mean you no longer need the magnet on the back of the coil to get it going? You can hook the DMM to the negative side of the battery OR...

when you place the magnet on the back end of the coil is the magnet side that is facing the coil the same polarity as those on the wheel as the face...

I'm curious what is leading you to believe it is in attraction mode, and what leads you to believe when you add the magnet to the back of the coil...

Must not have had enough resistance on the base for it to melt like that. I found the pendulum to be the most basic build for learning balance: