I realize there's a few zillion threads about knock in 4.x motors, but I haven't seen any yet that do the same thing that mine does.

When started cold after not running for a few days, it'll make horrible loud noises for 10-20 seconds, then it'll go away. If let idle for 5-10 minutes, it comes back but nowhere near as bad, nearly inaudible, you have to stick your ear right down in the engine bay to even hear it, but if I leave it idle for another 10 minutes or so after that, it completely goes away and the engine sounds as healthy as the day I first heard it 12 years ago.

Note that the gas in the car is not the greatest, there is EGR buildup, and the car sat for nearly a year without being started up until about 5 months ago.

Besides the obvious gas/egr problems, what else could this be?

One time, my fuel pump fuse blew, and left me stranded (didnt know what it was). I pushed it into a parking space (engine off), and came back the next morning, after letting it sit overnight. Well, it had the loudest most horrible clacketing/lifter whatever noise in the engine it's ever made. This continued 5-10 minutes, as I grit my teeth the entire time wondering if I should let it run or shut it off. Well, after idling it around the lot a little bit, in 10 minutes it went away, and has never come back. There were about 50,000 mi on the new engine at that point.

The only thing I can think of, is that maybe pushing the car (with engine off) may have drained a lot of oil out of the lifters (dont ask how), or maybe something got out of adjustment. Not sure if I put it in neutral, drive, or a combination of both while pushing it into the space. Maybe oil pump wasn't working while pushing, I dunno.

Bottom line, is maybe it had to do with the oil--could have got sludged up and is blocking oil from getting to the lifters, who knows. Maybe try changing the oil, and if that works, change it again within 1000 or so miles.

there is EGR buildup, and the car sat for nearly a year without being started up until about 5 months ago.Besides the obvious gas/egr problems, what else could this be?

Well dude, you've pretty much just answered the question to your own problem. Fix those problems first and see if it goes away. If you need help on the correct EGR cleaning procedure, either myself or someone else will surely be glad to help. Also check your timing and such: you can never be too careful.