I am way out on a limb when I suggest this, so take this as a crazy idea. Rather than doing a database overlay over an existing stable filesystem, develop a new experimental filesystem that has a database-like interface.
For example, in Linux a certain amount of your storage medium is devoted to inodes, which holds a table of meta-information about files. And there is some software which links the inodes with the files.
What if instead there was a section of the storage medium that held a database? The database contains meta-information about the files. And then there is some software allowing you to find files by querying the database. It could be much more than a lookup table.
One other way of saying it is that the existing tree-like hierarchy is a simple and useful paradigm. What if there is another paradigm out there that is more useful?
How Does This Relate To Multiple Ways To Sort Files
I would think that if a person went to the trouble of implementing something like this, they would do it partly because they wanted to change the way we deal with files.