For example, I want to really learn the NATO phonetic alphabet, and I have a card for each letter, but I'm still slow when I spell things out.

This is one of the things that might benefit from social learning. Find a friend that also wants to learn it and play around with it together. I learned the entire alphabet during an internship with a local police force and it never slipped my mind since. It's something that you need to use in order to memorize it.