Thanks for the replies. I was considering one of those carts, but it seems like the wheels are sub-par. Instead, I found this:
https://www.walmart.com/ip/Super-Stacker-Document-Box/36573022
which is perfect because it fits most every tool (I have some big hammers and a plumber's wrench that can go in my old canonical toolbox), and it's shallow enough so that tools aren't more than a tool or two deep.
I'm going to build my own dolly using planked 1 x 10s (or whatever) & these wheels:
https://www.amazon.com/gp/product/B085RQFMYR
So I will be able to fit every thing heavy in 6 of the boxes, and have them stacked in a pair of 3s, allowing me to even put another box on top, which will have all the soldering stuff. Perfect. I haven't even built the wagon, but just the 6 boxes have immensely decluttered the area. (The only clutter now is pin parts that I need to install, LOL.)
I still have 3 of these caddy things:
https://www.amazon.com/Alpine-Industries-3-Compartment-Plastic-Cleaning/dp/B07NVWK2VX
for stuff that stands up like Wildcat cleaner, Novus, Noxon, WD-40, etc., and for jumpers & multimeters. These things have some volume to it, so I can't so neatly densify them, and the handle makes them very portable. A battle for another day.