The whole thing about big music programs like iTunes is that you don't have to care about where the files are actually kept and in which folders, your player just gives you sortable data that you can display and manipulate however you want. Personally I always go with Artist -> Albums Sorted By Date, but some people like genres and whatever and use playlists a lot. But it doesn't matter, you just throw your various folders of music in one big folder and point your player of choice at it and it goes and identifies and creates a database of all the music. Programs tend to call this a "Library", perhaps you've heard of this concept?
At that point you can use Amaork, Clementine, Tomahawk, whatever. Doesn't matter, any of them will trawl through the folder(s) you tell them to and give you a library listing that cares not one bit about how messy or not the actual files and folders are.
Why do you care about your music program sorting your files into nice ID3-based folders if your interface to them is completely agnostic towards the file structure? And if you do, then just write a quick bash script or something and install a non-Library based player like Audacious if you like interacting with your music collection in a folder-and-file way.