So in order to play 400 holes playing an 18 hole course its 22 rounds and a couple extra holes. I would imagine that it would have to be on say the summer equinox for maximum sunlight. Just depends on what your average time per round is but I'm guessing you would need to average 45-50 minutes per round at the slowest.
I know your crazy enough to do it though, or at least attempt.
it could probably be done but in the lower 48 your sunlight is shorter than here in alaska.the summer peak here is close to 18 hrs of playable sunlight ,ive played a round as late as 1 with dim but usable light .i dont think it can be done here because the one course short enough here is also the most popular with close to 300 rounds a day in the summer.there would be no way to avoid the backups at the tee's which can be 5 foursomes thick.but i will try to break my best of 72 hole on 3 courses next yr