You are forgetting they made an newer instancing system that allows for many more instances? It is used in assault, salvage and some WotG missions. SE could of used this instead of the older BCNM system for shinryu however they probably wanted to save server bandwidth and use the older system that supports only 3 fights at once.
Personally I only seen Shinyru congested once when HoA was still new and a bunch of people were doing him.