Click the mind control thing from the ground below the platform. Run Razorgore up to the platform with the mind control thing and run him into the wall all the way in the back. Let him sit there for two full mind control casts and do nothing other than dismiss him before it expires.
Dismissing him as a pet will cause any agro'd mobs to focus on you and if you do nothing through two full rotations the mobs reach spawn limit and can't spawn anymore. At that point you can run Razorgore around freely and kill eggs
To be safe, let the mobs all go away and despawn before killing Razorgore. Sometimes if you kill him to quick it bugs out.