Seems like you are obsessing about the wrong end of the stick. A 1 to 2k jump or another 1k is a sideways move, yea it is better, but just go to a 4-6k and make a real difference.
The real goal is to get to an 8k finish/edge, or as close as possible if you jump to naturals. Look at your edges, it does not get straight until 8k.
Get the bevels flat and in the correct plane and meeting with whatever it takes, 600-4k, (depending on the razor condition), as long as you remove the deep stria completely and start polishing.
8k is the game changer. Then it is just polishing. 8k to a natural is a piece of cake, or can show that your “Natural” finisher is not better than an 8k.
1k to a natural can be done, but it is all about the stone and technique, (slurry). A good Jnat can easily remove any 1k stria in about 40 laps, so it is totally about the stone and technique.
Slurry is a double edge sword, it can multiply stone grit, but will also edge impact, dull and chip an edge. Try setting a bevel on a 1k with slurry and look at the edge, now wash off the stone and do 20X laps and notice how even the stria pattern becomes and how straighter the edge becomes.
So, even with an aggressive 1k how deep the stria is, can be more about technique than the grit in the stone.