Most of the noise is coming from the cassette/rear derailleur area. The chain is visibly clicking on the lowest cog. I've adjusted everything; limit screws, barrel adjuster, b-screw, etc, so everything is lined up correctly. I've taken the jockey wheels off, cleaned them, put them back on. Still noisy. The bike is brand new, so the cogs and chain shouldn't be worn. On the other end, when pedaling hard on the workstand, the crank makes a deep vibration and the chain shakes between the cassette and the big chainring. I haven't had an opportunity to actually ride the bike yet because of the weather, so I'm not sure how it actually sounds on the road. At this point I've pretty much given up, and I plan on taking it to my LBS. Any advice or suggestions would be appreciated.

Are you sure the chain is threaded around the rear derailleur jockey wheels correctly? There's a little tab that the chain must go on the inside of, and I once put it on the outside of that tab, and everything worked and shifted, but it rubbed on the tab and was noisy.

Chain routing through the rear derailleur pulleys, like tyrion described, is my first suspicion. I think there's a pretty good chance that's the problem. If not, we need to question the assertion that "everything is lined up correctly" and go through the process of setting up drivetrain adjustments from scratch.

Checked the chain and it's routed correctly, on the inside of the metal tab. One-eyed the alignment of the jockey wheels to the cogs again, and they are straight on.

Turn the crank slowly backwards and watch as the chain comes off of the lower rear derailleur pulley. If there is a tight or damaged link you will see it as it will not straighten out properly as it leave the pulley.

Take it to the bike shop seems a good idea, better than long distance guesses.

Checked all the links, they're clean and move properly.

The test of the pudding is in the eating.

I wouldn't get too worried until I had chance to take the bike for a good ride. If it still makes enough noise to bother you, that's the time to take it back to the shop where you bought it.

Does this happen in all gears, or only on the lowest (largest) cog?
You are sure the chain is brand new?

I don't mean to be insulting, but eyeballing jockey-to-cog alignment isn't how you're adjusting the derailleur, is it?

Might I suggest Park Tool's rear derailleur adjustment procedure? Follow the process from A to Z, without skipping, and it'll get you shifting well more often than not.
https://www.parktool.com/blog/repair...eur-adjustment

Yes... it is haha! No offense taken, I'm just completely inexperienced at this kind of work. The chain is actually clicking at the top of the smallest cog - not at the bottom, where I'm guessing a misaligned derailleur would pull the chain into the next cog from below. Hopefully I'm making sense.

Someone else may have mentioned it, but your H limit screw may be set too tight. If it is the rear derailleur cant move out enough. Then the second smallest cog may be fine, but not the smallest one.

I suspect that the key clue here is the vibration in the upper chord when on the smallest sprocket
(exclusively?).

I read that as indicating an engagement/disengagement issue, possibly caused by the rollers touching the corners of the next tooth as they swing clear. This really isn't all that rare on brand new drivetrains, because the smaller sprocket makes this a critical tolerance zone.

The good news is that the least amount of wear (hours, not days) will break down the corners, and also increase free play at the rollers, either of which solves the problem.

Other factors may include chain line and/or burrs on the sprocket teeth.

In any case don't obsess over this yet. Ride the bike long enough to break in the drivetrains and see if it resolves, before wasting time over what may be nothing.

q. e. d.

Managed to figure out the clicking, so now it's the just plastic-y sounding jockey wheels and vibrating crank that are bothering me. But, from what I've read about new bikes, after a few miles those sounds should settle down. Just gotta break in the drivetrain a bit, I hope. Thanks for tolerating my inexperience everyone.