I think everbody is frustrated because nobody has figured this mess out yet. I'm going to give you my best guess based on what I saw on my engine and what you say you know about yours.
When I got my car I knew it had bad CATs and a damaged engine. I like you knew the sound was coming out of the top end and tore the thing ALL apart hoping I could fix it before I decided to go with the salvage engine. I could not find a single thing wrong in the valve train, NOTHING! Now, after the final teardown and some more research I do have my best guess.
The VVT system actually varies the timing of the hydraulic lifters by sending oil "to" and draining oil "from" the a set of chambers in the actuator. To get there, the oil has to pass through a series of 3 very fine mesh screens. These screens create a large resistance to the flow of oil and if it can, it will flow elseware first. As I show in my pictures, my oil pump had large scratches/grooves in the side walls which more than likely allowed leak-by resulting in a lower oil pressure supplied to the engine. The oil plumbing system in a car is just like the plumbing in a multi-floor house.... the water pressure is always highest on the ground floor and lowest on the second or third. If you are showering on the second floor and somebody runs a sink down stairs, they get the pressure and your shower slows to a dribble.
If your car ran low on oil long enough to damage the oil pump (lower the pressure) and damage the main crank and connecting rod bearings resulting in larger clearances allowing more flow through them (like somebody turned on a sink downstairs), I believe there is not enough oil pressure left to operate the VVT system correctly and inflate the hydraulic lifters so they end up running completely collapsed and rattle like a bitch. To support my theory I refer to post from people who installed an incorrect/cheap oil filter that did not have a reverse flow preventer diaphram and the oil could drain back out of the valve system when the engine was shut-off. They all reported terrible valve clatter for the first 20-60 seconds until the oil system filled and pressurized.
So what should you do????? (Presuming your engine is torn apart and not runable.) First I would remove the oil filter, cut it open with a chisel or actual oil filter cutter (it is like a can opener) and inspect the filter media for metal. You may have to cut the filter paper off the core with a razor or steak knife and lay it out flat on some paper towel. This will give you the best report on damage. Second, remove and inspect the oil pump for damage. Third, if you find metal or damage, then remove and inspect some connecting rod bearings.
If your engine is runable, then the first thing I would do is tee in an actual oil pressure gauge and see what you really have.
There it is....that's my theory and I'm sticking to it.
