Funk, your black may still be a finisher, Blacks and translucent do not leave a traditional stria, but a kasumi, hazy pattern, which is why you cannot grit equivalent rate them. They will or can finish much higher than their rating and as said can be burnished to finish even higher.
You have to get rid of all the stria from 200 up to 1k diamond before you can even attempt to finish with the Black.
Are you considering purchasing a new stone or are you trying to accomplish this with what you have?
What kind and power, of magnification do you have?
If you are determine to do this with your existing stones, try this…
Double tape the spine and do circles on your 1k Dia Sharp in sets of 20 until you remove all the low grit stria. Do not use a lot of pressure, water and a drop of liquid dish soap will help, it should not take too long, but you do not want to create deep 1K stria.
Once you remove all the deep stria, do X laps, on water with weight of the blade until you get an even 1K stria pattern.
Lap the soft Ark on an 80 grit belt, for arks grid mark them with a Sharpie, pencil washes off too quickly. Work up to a 400 or 600 grit progression.
Now do circles on the Soft Ark until all the 1k stria is removed. Then lightly joint the edge on the corner of the soft ark. Just lightly drag the edge on the corner of the stone. This will straighten the edge.
Now do x laps until the bevels come together again and an even stria pattern is on the bevels. This may take several hundred laps. You may not get all the 1K stria off, you Soft Ark may be too course. Either way you will reduce the 1K stria and straighten the edge.
You should have a straight edge and even shallow stria pattern on the bevels.
Lap your Black Ark as flat and smooth as possible. Now remove all the Soft Ark stria with the Black Ark, here again hundreds of laps.
As said a Norton 4/8 combo stone would make your life so much easier.