A good possibly is the valve covers gaskets need replaced & the vvti O-rings come w/ the valve gasket.

 

See this video regarding what this mechanic did to stop the death rattle without tearing the engine apart. It is similar to what the OP figured out.

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Awesome video Clutchless!

Another dozen cold starts later and still no rattle, and my rattle was BAD. It had to have been the timing chain rattling around from a loose timing gear system due to no oil in the vvti cam gear. I always worried about it causing major damage. I'm so glad it is fixed

The original thing that clued me into the typical approach missing something big was when it first started happening and I kept the rattle at bay for months just by putting the key in the ignition and turning the car on without starting it, and letting it sit like that for a minute or so. If I did not do that it rattled every time and if I did do that it rarely or never rattled for months, and it got progressively worse until it rattled every other time no matter what. Then I started pulling the fuse to fill the vvti cam gear with oil using the starter, which worked great aside from burning through a starter (easy replacement), and now it is fixed all together. I highly recommend this repair to anyone. Here is a GREAT detailed video to help.