Congrats on the new toy!
Your grind setting may need to go coarser, depending upon your individual grinder calibration halfway (20/40) may not be coarse enough. I run about the same coffee water ratio, (within a gram or two) and it will come out noticeably sweeter and cleaner (less bitter extraction) at coarser grinds. You can tell when you get too coarse as it goes a little sour in the cup. (or until your grinder can't handle the gap and starts kicking out tons of fines)
I also divide my pour into 3 sections:
1 > The first is the pre-wet, get it nice and soaked and wait for all expansion/air/bloom movement to stop.
2 > The second section sets up the filter bed, you can spiral around a little to distribute the grinds, but go very slowly and close to the top of the coffee.
3 > The third section is faster pouring, but only in the very middle. I try not to change the level of the slurry but want to get the entire pour finished (including blooming) within 3 minutes. Stay close to the top of the coffee and don't disrupt the filter bed layer of coffee lining the Kone.
If it already tastes good, and you can easily control your brewing time with large and small batches, then don't worry so much about the sediment! Enjoy your new Kone!