It's possible, but tricky, to do it if you happen to be:
- a hunter
- a goblin
- an engineer
- a demonology warlock
The trick is to aggro Razorgore, then jump from a ledge near the Grethok the Controller to a balcony. Once on the balcony, Razorgore will continue to attack you, but Grethok will call off the alarm, preventing adds from coming in to kill Razorgore:
As long as you quickly kill Grethok and the other two orcs, and stop controlling Razorgore once you hit ~25 seconds left on the Mind Exhaustion debuff, you can destroy the eggs with impunity and take Razorgore down.
Hunters, Goblins, and Engineers
To jump to the balcony, you need to use:
The YouTuber Shopebay1 put out two videos demonstrating the basic premise.
As a hunter with Disengage and a parachute:
As an engineer with Nitro Boosts:
Note that I found trying this with the Nitro Boosts to be extremely frustrating: you only have a few seconds, it's prone to failure, and it has a three minute cooldown, meaning if you don't make the jump it's a wipe.
Demonology warlocks have it easy. Before pulling Razorgore, make the jump using Demonic Leap. Once on the balcony, summon a Demonic Circle. Then, pull Razorgore: once you're in range of the Demonic Circle, pull one of the orcs and teleport. Then, follow the same strategy described above and demonstrated in Shopebay1's videos.