What does the run look like, is it just two dimension length x width? Because while it will look more cluttered, it is much better if you take a look up at the third dimension. Add platforms that birds can get under or stand on top, add roosts in the run, add some hideouts. While these will make the run look cluttered, it gives the birds a lot more room to get away from each other.
Go in there and jazz it up with some pallets, limbs, ladders, chairs, whatever, and then mix it up like Junebuggena says. It will all help.
Mrs K