I'm surprised nobody has thrown out the idea of force carbing the entire keg, then just bottling from it. You can do it as simply as a bottling wand stuffed into a picnic tap with the springy bit removed. I have a beer gun, but for 6 bottles or so its not worth breaking it out. I do this all the time.
Advantages are clearer beer in the bottles (no sediment), you know the carb level, and it's faster.