I had a bunch of loose end mills of varying quality and sharpness that I transferred from larger plastic containers to drawers in a parts cabinet. To protect them from further damage, I cut pieces of thin cardboard (like manila folders or index cards), wrapped them snugly around the cutting edges, and then used tape to keep them in place. Then I crimped over the end, added another piece of tape, and "Bob's your uncle". It's also easy to write the details of the mill on the outside, and the mills can be packed tightly together to save space.
The ice cube trays are probably good for mills you use a lot so they can be accessed easily.
Something else that I might try is using
XenoPoly to coat the tips and cutting edges of tools. It is a very soft, pliable, non-toxic plastic material that can be used for confectionary molds, and it melts at about 275-300F. I could probably heat the tool with a heat gun and then push it into the plastic to coat it. Then I could also use the heat gun to melt the coating off, and it is re-usable. It should work well for small items like drills, taps, and reamers.