Hindsight being 20/20, you should have posted this in your first post!

But hey, it was a good convo along the way, so it worked out great!
I was first going to suggest you lower that wooden shelf that's there to the top of your highest bin or bucket. Until I saw how reinforced it is. I'd leave that right where it is! Then above, you could put your cupboards or more shelves, whatever you think works best.
Under that shelf though, for shorter stuff, you could build a shelf. Here's a YouTube for a
rudimentary one, which is all you need.