I'd like to add my two cents without having read the discussion. We're talking about a "Melee" type trying to get a "free" attack by taking advantage of the ambiguous term "dropping" an opponent.
I'd like to say that, as a DM, I don't think I'd care all that much as long as the Cleave attack was on someone other than the target tripped. My reason for thinking that is, quite frankly, Cleave sucks.
Let's look at the feat "Curling Wave Strike" from Stormreach. It allows you to make a second cleave trip attempt. Isn't that quite like how cleave would work in this instance? Instead of making a cleave attack you make a second trip attack.
House ruling it, I'd say Cleave would work quite like Curling Wave Strike.