I would try to limit the noise happening to the top-end or bottom-end of the engine.

I have heard noises similar to this with broken/cracked valve springs, but never from the 3.4L. If that isn't the case, and P/O beat it to the point of needing this much of a valve adjustment, I would expect it to have a warped head/bent cam.

I am not familiar with exactly how the cam preload works in these, but the machine shop I use has told me that not setting the 3.4 cam preload when putting the engine back together will cause a noise exactly like this, so it could potentially be that or the spring that it's preloaded with malfunctioning.

If the noise is bottom-end, I wouldn't even bother buying it unless you're good with doing an engine swap.