I’m going to go out on a limb and say timing chain. If it wasn’t drinking fuel at such a large rate, I might blame the fuel system (might have the pressure at the fuel rail checked, just for the heck of it), but this has all the classic symptoms of timing being out of whack. Either the chain is off a tooth or it’s just got too much slack in it.
Did this just start all of a sudden or did it occur after another event?