Just to check: does this run have a roof?
It is sounding to me like your predator-proof "run" may actually be a perfectly good open air coop. If that is the case, I would leave the eglu door open all the time, and let the chickens choose where to sleep. Some of them may choose to continue sleeping in the eglu, or they may all choose to sleep out in the run and just use the eglu for laying eggs. Either way, as long as they are protected from predators and rain/snow and have some shelter from heavy wind, they should not have problems.