I went to Lowes and talked with a guy about what I was trying to accomplish (shelves inside the cupboards that are more easy to reach. He was amazing and looked in a million isles with me, brainstorming a bunch of different ideas and options. Finally he remembered a newer product they had, industrial strength Velcro that can stick to most any surface, even rough ones. I went to the dollar store and found baskets that were just the right size.
Because the baskets I found had open slats, and I wanted the sticky back of the Velcro to be able to stick, after sticking on the Velcro, I used a thin plastic vinyl (found at any fabric store) for the inside of the basket (so the Velcro went on the outside with the sticky part facing against the outside slats. Then, the Velcro went on the inside, across the slats and stuck to the stick part of the Velcro). I used the baskets on the walls, so that they would be easy to reach.
Next I added our play cups, plates, utensils, and bowls, so that Madi would be able to reach them easier.
I'm not done yet, I just ran out of Velcro and baskets :). My plan is to add a few more down below the others and also add a few inside of the cupboards that will open out when the cupboards are opened. I'm glad to have such an easy and fast solution, though! So far, it's working out well!