All of my cleaning rods are 1 piece (including my trusty TICO tool). I have a .17 caliber rod I use for my .204, another that is good for .22 to .264, and another for .277 and above. I also have a 1 piece shotgun rod for brushes. I also use an old tackle box for patches, brushes and smaller bottles and cans of cleaning fluids. The tackle box also fits my pistol rods. 14" contender barrels have always been a pain to clean since my pistol kits aren't long enough. I learned to just clamp them in a vise and use the rifle rods.
I also have a Tipton Gun Butler that usually has some extra scrap rags, bigger bottles and other stuff I didn't get properly put away in the tackle box. I like the tackle box and the Tipton as they both have handles and can be stored and moved easily.
Having all those one piece rods, I wound up just storing them in a display gun cabinet (pictured) that on of my Dad's patients built for him when I was a kid. I keep a few odd guns in there that I no longer have room for in my safes. The empty spot is my .22 Mag that is temporarily in my garage for Hogs.
At the beginning of lockdown, I went through all my cleaning stuff and got it more under control like you are trying to do now. I know I have cleaned all of my guns since March, so a few things are in the Caddy instead of the tackle box, but I feel that it has been easier to keep things neater since.
I do seem to be able to get all of my loading, ammo storage, cleaning supplies, etc. into a state of disarray much quicker than I neaten in up.
Good luck and all the best.