By putting a thin spudger between the two halves of the plastic container, it is fairly easy to separate the two halves. But the top likely won't come apart without a fight. There are two primary pieces to keep in mind:

The small clips that show "L and "R" should probably be removed before the two pieces are separated. They are clipped into the outer shell and adhered with a similar adhesive to the outer rings that were previously removed. The trick: spread one side outwards as you are prying the broad section away from the rest of the shell.

Now to the main issue: there are deep "tracks" that clip the two halves together. I haven't been able to use a technique to make this easier, as you cannot "slide" the two halves apart. Just like the L/R clips, concentrate on stretching the inner (grey) part as much as possible. Force will be necessary; leave a comment if a better way is found.

You may be able to separate these pieces once or twice, but they do bend slightly and eventually the rails will deform, making reassembly impossible without modification.