I ended up with 12 Kar Products and Lawson Products assortments from a retired mobile mechanic. He kept them piled on shelves in his truck, so they didn't come with the racks. I have hated unstacking them to get at the one I need, so when I saw an old airline meal rack for sale on Craigslist, I checked it out. It was a little too narrow to hold the boxes the normal direction, but by putting them in the long way, there is plenty of room to put a small assortment or two next to each one.
I figured out that the optimum shelf size was 1/2" thick, and was able to make all the shelves I needed from fall-down from old projects. I'd hate to buy the plywood at today's prices! I added a full-depth shelf from 3/4" plywood at waist height to pull out and set the box I'm working with on. I had to bevel the edges of the 3/4" to get it to slide properly, but it does with no slop.
I had to relabel the assortments on the ends because the regular markings aren't visible. Now, I open the door and can see what I want, pull out the shelf, pull the kit and place it on the shelf, open the lid, and pick the part!
Best of all, it is on wheels and rolls easily, even when fully loaded.