Yes, there should be smaller eddy currents formed when the tube has a slit in it. Those same eddy currents will also be formed in the tube without a slit, on top of the current that goes all the way around the circle. The important thing is that the primary current gets cut off by the slit, reducing the amount of energy dissipate compared to the slitless tube.
So, the answer I would expect to be correct would be that the falling order would be: plastic, slitted copper, and slitless copper.
That the answer comes out as the slitted copper and plastic ring hitting simultaneously isn't too surprising to me because the eddy currents in the slitted ring are quite small, and don't dissipate enough energy to slow the object down significantly. It's kind of like dropping an orange and a bowling ball at the same time - the bowling ball experiences more air resistance, but it should also have a higher terminal velocity because it has more mass.
It would be interesting to see this experiment done with a very long drop viewed by both high speed cameras and thermal cameras.