This might be beyond my skillset... But I would try this:
1.mill the ends down flush to the sides.
2. cut a new lid the exact length of the whole box
3. mill a lip in each end of the top the thickness of the angle stock
4. mill a lip in each side of the top the thickness of the channel stock
With little filing and fussing the lid should sit on top of the box recessed into the box.
Like I said maybe beyond my skill.. but be fun to try!
It might be beyond your skill set when you start, but if you are serious, it will be within your skill set when you are done. Go for it!
Rick