Just surfing through the threads and seen your post. The outer diameter of the shroud is about 1.1 inches. About 1 1/8". I have a Denall suppressor and it is 2" diameter and have plenty of clearance to see through the sights. 2" is pretty large but I would not go much larger. I am not sure if he is making them any more.
BTW you probably need to get a new shroud and barrel nut. (since the nut is captive. If you want to keep the original parts.) To thread the barrel you need to cut the shroud down ( The shroud is the same length as the barrel) I just went with a new barrel too. The Denall suppressor is a little different. The barrel threads into it a few inches. (Maybe 3" just a guess)