I've done a lot of 200-mile rides, but have never managed to hit a 100 miles in 5:30, either, and don't expect to anytime soon.
Anyway, the 200-miles is generally not a problem, just plugging along till you eventually get there.
Now, if you want to be fast/competitive/#1 etc., THAT's a problem.
Find you a 200-mile route with adequate stores along it, get you some good lights if you don't have them, go ride 200 miles a couple of times, don't worry about speed, get a friend or two along if possible. Stop and take pictures as you feel like it. This won't really prep your body for anything, but it'll set your mind at ease. Then you can start worrying about how to do it better or faster, instead of how or if you can even do it.
If you live anywhere close to one of the 12/24 hour lap races, go do the 12 hour as another option. At your speed, you'll be close to 200 miles if not there, just pace yourself and use it as a learning experience.