Since this is my thread I'll update what I ended up doing here.
Cleaning a chain on the bike is a disaster. It turns out that using a scrub brush, toothbrush, pressure washer or soap just doesn't remove enough of the accumulated wax/crud that keeps piling up if you don't thoroughly clean the chain. I suppose I could use kerosene but that'd mean a) buying some kerosene and b) dealing with the smell of it.
I bought some Tusk master link pliers and they don't work well at all. I did it the old fashioned way with a hammer and the flat end of the tire iron to remove the link, and then used regular needle nose pliers to put it back on.
On the advice of a few YouTube videos I needed to get all the waxy gunk off after a year (!!!) of not having a really good off-bike cleaning and there were some tests done that essentially said that either dedicated bike chain cleaners (e.g. the FortNine videos) or some Zep Pro Degreaser from Home Depot or L.A.'s Wonderful from the dollar store would do the trick. I put straight Zep Pro degreaser in a container and sloshed the chain around it it. Then I took the toothbrush and scrubbed end to end. Lesson learned, I probably should have worn gloves for this because the Zep instructions said to dilute it quite a bit before use and that it was quite alkaline - my hands felt just like they'd been dipped in bleach.
After rinsing everything thoroughly with water I then sprayed CRC food grade lube on all 4 sides of the chain and let it sit overnight. Next morning I wiped it off with a paper towel to get most of it off, though it is still quite slippery.
Results:
So, from a distance it looks super clean. Zoomed in like this, I can see all the little spots of dirt I missed lol! I'll get to those next time, but I'm amazed to see the chain is silver in color and not black.
I will spend some more time on the sprockets too.