Ah, I figured it out. Perhaps Googa was referring to a different version of this room in his hints, because my solution
Click here to view the secret text
×does indeed involve sacrificing an elemental, though not as you might first suspect
and also
Click here to view the secret text
×does not involve striking both orbs simultaneously.
And it was a really obvious solution, too.
Hints for future travellers:
Click here to view the secret text
×There is more than one way to skin a cat. When the time comes, go for the direct route.
and
Click here to view the secret text
×When I asked if there was some way to get the two elementals out of rotational sync with each other, that turned out to be completely unnecessary due to an obvious action available to you. See prev. hint.