(weird, getting a server error when I try to post my complete post, so I'm having to do it piecemeal. So, here's part 3.)
So-- if after the gravel cleaning what you had was an ammonia spike, perhaps accompanied by a bacteria bloom (cloudy tank), I'd say you simply released trapped dirt and nutrients into the water, causing the ammonia spike.
But-- since you're detecting nitrite and not ammonia, then probably you directly released the nitrite stored in what effectively was the de-nitrifying area of your substrate.
The sudden and anomalous release of extra nitrite was more than your beneficial bacteria in your filters were prepared to handle since the bacteria colonies grow only to whatever size the available nutrients will support, regardless of how many filters you have going. Thus, a nitrite spike.
From
Seachem regarding nitrite production in low oxygen conditions:
There are two types of denitrification that can occur: ammonification and anoxic denitrification. Ammonification results when there is no oxygen and anoxic denitrification results when there is low levels of oxygen. Both result in the conversion of nitrate to nitrite and then eventually into nitrogen gas which can gas off. Ammonification can create ammonia as the final product.