Yes to U shape shelves and also add more shelves. My theory is everything possible should sit directly on a shelf or fit inside an organizer of some type. In my previous pantry I had a couple taller shelves which had a short shallow shelf across the back. I think I used a 1 x 4 and put it about the height of small cans or gelatin boxes. Nothing gets lost in such a small spot. 
In a pantry your size, I would use five or six shelves of differing heights and depths. Floor can store drinks and other bottles like vinegar. If you have kids, put their snacks on a low shelf. Next shelf up might hold baking supplies so height can be an inch taller than a bag of flour. Have a shallower shelf for cans and jars, tall enough for quart jars and only deep enough for three rows. I had a top shelf about 6 feet tall where I stashed unbreakable, easy to grab items like cereal boxes and paper towels. I had a door mounted metal rack for bottles and cans. 
I use the same strategy in my dish cabinet where I added an extra shelf just tall enough for mugs.

prefer a blended approach. add a shelf in lower position. add a half shelf at the top if you have distance to ceiling. the half shelf can hold big tubs of things you dont need access to very often. So if you start with four shelves and the additional half shelf...maybe one or two U shaped. the other two could be full depth and add glides with a tray or box that slides out to you for retrieval. I'd get the wire shelf organizers that are inexpensive to stack all the other stuff better. doesn't matter if its your existing shelves or U shape shelf ...the stacking can be done better with all the different shapes and sizes of the wire organizers. Try [ container store] or [kitchen source] or [ organize it ] ... sites that have pantry and cabinet organizers. If you dont want to spend for glide outs, or to redo to U shape, you can accomplish a lot with an extra shelf and organize things . the glides with trays or boxes will be a benefit if you have good depth.....the depth isnt described and its hard to tell.

Add shelves and organizers. I have can holders, lazy susan for the shelves to hold jars and bottles, and assorted undershelf baskets. You should definitely have a set of the airtight storage containers. You might try an L shape rather than U your pantry doesn't look wide enough to handle U.

I have a tray on the floor for oils. I keep them in bags and on the tray because no matter how careful you are they drip. The floor is also good for the large box of garbage bags, paper towels and pet food.

I had a pantry about that size. I put 8” shelves so that things didn’t hide behind each other, and spaced so two cans could stack, or to hold my tupperware containers of pastas. and a 12” higher up (for paper) and also an 18” deep shelf above the floor for cereal and other bigger things. Then, a rack like you have on the door, but it was on the left side wall. Perfect for cans, etc. Mine wasn’t wide enough for a U, things would have disappeared and been inaccessible in the corners, The rack was shallow enough that all storage space was accessible.

Now that I have an even narrower kitchen pantry but also a basement, I created a ”backup” pantry down there using Target bookcases, so in the kitchen pantry I have one package each of different pastas and grains, cereals, or vegetable and soup cans, and the basement makeshift pantry holds the ”next” package or two (or more) of those things,

When I make my shopping list, I shop in the basement first. If I’m down to the last package of something there, it goes on the list. So the kitchen pantry only holds the items in current use.