I've now changed strings on my slotted headstock twice, and the second time was a significant improvement over the first. Here are some things that helped me immensely the second time.
1. Get yourself one of those Planet Waves Headstands (or similar product) so that you can work on restringing the headstock while it's raised in the air. I generally lay the guitar on a towel, prop up the neck with the Headstand, and hang the headstock over the edge of a counter so that I can work on it from underneath.
2. Get yourself one of those Ernie Ball motorized string winders. It's a godsend.
3. Thread the string through the tuner hole, allow the proper amount of slack for that particular string, then clip off the string about a quarter-inch from the tuner capstan (this will keep the string from chewing up the wood as you wind). Bend the excess quarter-inch of string back toward the bridge so that it can't pull through the capstan as you begin to wind it. Then use the motorized winder to bring it close to tension. Clip off the excess quarter-inch of string as closely as you prefer.
4. Rinse. Repeat on other strings.