My solution may not be the best, but at least it doesn't take up much
valuable space in my shop.

I have a melt pot of resin protector for cutters. Every one of my cutters
gets a dip after I purchase or resharpen them. To remove the cutter, I slice
the resin in a couple spots and remove it without ruining the resin shape.
When I'm done the cutter goes back in the resin protector.

With the cutters in protectors, they are just stacked in drawers by size and
function. I label the drawers as to what's in it. One cabinet holds tons of
cutters this way.

Karl