So the first issue here is that Cleave (and thus Great Cleave) requires that your free attack follow up an attack that fells an opponent, and that the free attack be with the same weapon as the first attack. Per the rules, “A grapple check is like a melee attack roll,” but how much like an attack roll it is could be up for debate. If it isn’t sufficiently like an attack roll to make the grapple check count as an attack, the damage from starting a grapple step 3, as well as the damage your opponent option, won’t trigger Cleave or Great Cleave.
In your favor, those say that you “deal damage to the target as if with an unarmed strike,” or “you deal nonlethal damage as normal for your unarmed strike,” respectively, and those are weapons, and dealing damage with a weapon is a pretty strong sign of an attack—but it’s not clear. Those lines are more definitively useful if we accept that grappling is sufficiently attack-like for Cleave and Great Cleave, as they make a strong case for considering the “weapon” used for that attack to be the unarmed strike, which you can go ahead and use to start a new grapple on the bonus attack.
There is a similar problem if you have constrict—or balor nimbus. That extra damage comes from those effects, not any attack. Constrict’s damage might be considered part of the original grapple check—which might be considered an attack—but balor nimbus is definitely separate. And separate effects, not part of an attack, will not trigger Cleave or Great Cleave.
Regardless of all this, the attack your opponent option will. And if you use your unarmed strike for that attack, you use it again for your free attack. And you can grapple with your unarmed strike, and grappling can replace any melee attack roll, like the free one from Cleave. So that works.
The problem is that if you are required to use the separate attack your opponent option, your bonus attack from Great Cleave only lets you start the grapple, and you have to use a separate attack to actually drop him if you want to use Great Cleave again. Only if the initial check can trigger Great Cleave can you use all these free attacks to go through all your enemies. (Note also that your DM may well decide enough is enough and say you are out of free actions if you are truly trying to chain this to a particularly large number of enemies.)