Ever run an encounter with gargantuan+? Does gargantuan+ suck in 5e?

[Unoriginal]

You could have it begin at the edge of the greatwyrm's space, not the center. Thus with a 300x300 foot greatwyrm, a 60 foot radius aura becomes a 210 foot radius aura (sort of, it wouldn't be a true circle since it's emanating from the edge of a square, more like a 420x420 foot square with rounded corners). I believe reach already originates from the edge of a creature's space; IIRC I found one listed monster who has a reach that is smaller than their size, so if reach was from the center of their space they wouldn't be able to reach anything.

That's indeed how the rules of 5e do it. The aura starts at the edge of the creature's controlled space.

Otherwise auras would be worse the bigger you are.