by coincidence, the polish that I have is the farecla. I don't have the 200, only the 300 and 500. For both ebonite and acrylic, I wet sand to 320-400, and then apply the polish. Going to 600 wouldn't do any harm, but I wouldn't bother with the micro mesh grades. Black is probably the hardest to finish, partly because it shows up every imperfection, but my black material seems harder than any of the coloured stuff that I have turned- maybe a higher carbon content.
Other polishes may work- that is the only one that I have used.
You will be rewarded for careful turning, and for making sure that every trace of the previous grit is removed. Remove the scratches, and the dust produced at each stage. The 120 grit gouge doesn't seem so useful on ebonite. If I have a bad day on wood, I can often rescue it with sanding (as long as it isn't too close to the finished size). On ebonite, I would rather leave it to another day and try to correct the mistake with a tool. maybe that is just me.