The stepper gennys won´t power it, the voltage drop under load is simply too large.
Would however have assumed that the PMR would, without even breaking a sweat, being listed as 10V/1A.
Have you tried spinning it at high rpm (2000-2500) with a drill or similar, and measured the voltage then?
Might be an issue with the genny, as i do believe it should be capable of driving this.
...and in the opposite end of the scale, to much voltage won´t be good for the electronics either.
Would be wise to measure voltage as one speeds it up, to find the correct speed with no more than 5V DC (while connected to the plasmaball).