This is the general idea behind tags. You can choose to ignore one set of tags and favorite others. They are the means of categorizing content in the StackExchange system. It isn't a perfect solution since it doesn't allow us to force the choice of a "major category", but this might be something we could get adjusted since that functionality already exists on meta. I don't know if SE would go for it or not, but if people like the idea, I'll try pushing for it.
While your idea about trying to do sub-communities isn't a bad one, it isn't one that the SE platform currently supports. The change in design would require site specific development and would be more confusing rather than less confusing to new users.
Additionally, if anything, it would probably make the classification issues even worse for people. There is already enough confusion between the boundaries with Video Production and Music Practice & Performance. If we added yet another site to the fray, then it would be even more unclear which site is appropriate for certain questions and there would be a ton of overlap. For example, where would questions about things like compression, gating or reverb go that are applicable to both the recording and the live sides of things. Practically, I think this would result in more confusion rather than less.
Further, the pool of activity on both sites would likely drop to unsustainable levels. The merger happened in the first place to try to boost the amount of activity on both sites. I don't have access to the pre-merge statistics, so I can't tell for sure if it is better off now overall than it was before on the viewer and asker level, but I know that is one of the concerns.
I do agree that the communities have not really integrated well and there are still distinct communities within the user base that want both a more permissive and a less permissive scope. At the moment, the more permissive group seems to be slightly larger, but in general, we don't even get enough meta discussion to be able to determine which group really is more involved in the community.
I think this lack of involvement in discussing the issues is the primary reason that we've had trouble moving forward because we can't figure out what the community wants or work towards figuring out what the definition of our community is if nobody wants to talk about it. (So thanks for bringing this up again, and hopefully it will generate more dialog.)