Hi mattressjunkie,
Welcome to the Mattress Forum! 
There’s certainly no reason that what you’ve described wouldn’t work. And the fact that you’re basing this off of an already tried configuration is one of my top tips for any DIY mattress plan. Additionally, splitting the bottom 6" core into two separate pieces does offer you the flexibility to customize comfort now and in the future, and also create a bit of a “softer” configuration as compared to the Nature that you tested locally.
Mattresses.net is a site member here, which means that I think highly of them and their componentry. The certainly can be a good source for latex DIY projects.
Unfortunately, there is no specific configuration or type of mattress that is “good for fibromyalgia” in general because each person is unique, and a mattress that works well for one person with a specific condition such as fibromyalgia may be completely unsuitable for someone else with the same conditions to sleep on. In very general terms, softer and more pressure relieving materials that provide a more “relaxed” sleeping surface will tend to work better than firmer materials because for most people with fibromyalgia or arthritis a softer more pressure relieving sleeping surface is a more important priority, but I know that this does vary with individuals, as well as varying day to day. Latex and wool have been popular combinations mentioned over time here on the forum, but again everyone is different. A combination like you’re considering (and perhaps the addition of the shredded latex topper) can “put you in the ballpark” for people with such unfortunate issues.
A forum search on fibromyalgia (you can just click the link) will also bring up more comments and feedback from others that are in similar circumstances that may be helpful (but it will also confirm that there isn’t a single “best” combination of materials that will work for everyone with fibromyalgia).
In the end, nothing can replace your own personal testing, especially with specific health considerations. You’d obviously want to consider something that allows for enough surface comfort while sleeping upon your side and back, and also assists with pressure point relief, while still overall being resilient enough and provide enough support while sleeping. Overall, the two basic functions of a mattress are to support and to provide comfort (you can read more about that here if you like), with alignment being the first priority and then comfort coming second.
I’ll be interested in learning of your progress.
Phoenix