It may be beneficial to know where you're located. Perhaps there's an experienced member near you, whom you can meet, assess the situation in person and get some advice based on that. Just a thought...
From what I read, you sound like me. I.e. a DIY type of guy. If it were me, I would probably buy a good coticule and cover that entire "3 to 8K" range with a single stone. There are some advantages here:
1. You get acquainted with one of the most famous natural stone types in history of mankind. Seriously.
2. You may find it very useful for your knives
3. You may feel closer to being one with the nature, honing on a natural stone.... you know, Zen and all that... ;)
4. You get an actual finishing stone, that is capable of a lot more - in this case it will do exactly what you need it to do (mid-range), and then it will finish a razor, too.
5. You would then have 2 finishers, so you can get two types of edges, and can decide which you like more. It also means you can cover a wider variety of steels, possibly.
6. Because learning to *finish* on a coticule is not always easy, you have the Naniwa 12K as a safe haven to get back to, as you are learning.
Now, folks here tend to advise against the natural stones for beginners, for the sole reason they introduce a new variable into an already complex equation. But really, how complex is it? With all the resources available online, not to mention a potential mentor, if you publish your location, you could cut down your learning time significantly.
With that said, some reasons you should stay away from a natural stone:
1. You don't know exactly what you're getting unless the seller is knowledgeable and completely honest. This is no issue if you buy from a reputable member (say in BST here), but can't vouch for random people selling online.
2. Coticule is a stone that needs to be studied a bit. However, as long as it's moderate to fast on slurry, you are covered - you have your 12K. You have time to learn the finishing techniques on a razor, and this is actually quite fun, too (except when it drives you to drink, as we have recently seen here)
3. To be able to assess what kind of coticule you want, you need to invest some time to read and understand what people are saying. You need to learn to judge a stone by its appearance as well, because sellers, again, aren't always completely honest. You need to stay here for your learning, and not go on Youtube and Facebook much, because everything there seems to be "awesome", when in reality it is not. To me, this is by far the biggest challenge, and the only one that should keep a newcomer away.
If this sounds appealing, you should feel free to continue the conversation in this direction. Folks who have answered thus far know their natural stones very well, coticules included, so they are all capable of giving advice outside of the synthetic realm.
P.S. You've been given REALLY good advice so far, regarding the synthetic progression and options. I just felt like giving a different perspective, that's all. I won't mention Japanese naturals, which by the way seem like an obvious choice given you have high-end Japanese knives....