Electronic – Electromagnet with iron core seems to attract strong neodymium magnet when I want to repel

You could use a servo with a linkage arm to close the shutter. I'm looking at doing this right now, except I need to precisely control the aperture. A servo will give you (relatively) precise position control, and it's fairly easy to interface with.

If you need to close the shutter very rapidly, then your best bet might be a solenoid. I wouldn't, however, recommend building your own. There's plenty out there that'll do the trick and probably work better than you can design - it'll also save you time. You'll need to use a spring to restore the shutter to the open position. You might try searching Digikey.com to find some.

I'm hardly a motor expert, but since no one else has jumped in here, I'm going to offer a few thoughts as more of an "extended comment" than an answer.

Question #1. Am I dealing with eddy currents, or how could these odd scope waveforms be explained?

It's impossible to say, since you didn't say where these waveforms come from. How is the stator wired, and how are you driving the motor?

Question #2. I suspect that efficiency and field strength go up with steel placement, but why don't the plot field strengths seem to reflect this?

It did — inside the steel. Were you expecting the fields in the gap between the rotor and stator to change substantially?

Question #3. Whats the best way to understand these plots in a way that translates to real world physical force on the shaft?

Motor design is a complex subject, and as I said, I'm hardly an expert. The torque exerted on the rotor is a function of how much the energy of the magnetic field changes as the rotor turns. A static analysis of a single position isn't really going to tell you much.

The biggest problem I see with your design is the huge air gap between the rotor and the stator. You can see that lots of field lines are running directly between the poles of each, rather than coupling across the gap. This means that the total field energy is only mildly affected by rotor position, which makes the motor extremely inefficient.