Vancouver: you almost got it. you still have to have a short between the - of the first op amp and the + of the second op amp.
Keep in mind, if you still get some flickering in your ballast, you might have to play with your R1 and C values. Your r2 and your r3 values are good though.
Depending on the op-amp, it will only be able to drive the output within a volt or so of the power supply rails
Yeah thats why I told him to change the op amp supply voltages from 10 to 12 V