Ugh! I had that same problem. Trying to find a matching lid was impossible and opening the door meant an avalanche of stuff falling all over the floor.
I had the same set up cabinet-wise. What I ended up doing is buying 3 rubbermaid containers that are rectangular but pretty deep. They fit just under the shelf. 1 container is for lids only, and the other 2 are for containers. I put the odd shaped or really big bowls on the shelf.
We tend to use the same items often so they are usually just on the top of each container, but if I need to dig for something, out comes the container and I can search through it at the countertop instead of leaning over or sitting on the floor.
My stress of that cabinet has all but been eliminated!