I got up just before my alarm went off (old guy superpower) and flipped the meat one more time, to get the fat on the bottom and let that work a bit. An hour and a half later, I turned it off and moved it over to the larger counter to stand for a while with the lid on, to gradually come down to a workable temperature (pork that is a few degrees below boiling is
really hot). Here's a shot with the lid off:
You can see how the fat and connective tissue have softened up. After it had cooled, I started pulling it out of the pot - the bone came out cleanly:
And the meat came out in various sized chunks. If I had a use for the resulting broth I'd filter and save it, but it's not going to get used in the next couple weeks, so there's no point in keeping it around.
The meat then gets worked apart, with any larger pieces of fat and/or connective tissue being pulled out. I'm not super particular about getting every bit of that out - a little just adds some flavor - but I don't want a big bite of it when I'm eating a sandwich or a burrito or something.
The end result is a pile of pulled pork. If I was going to serve it fairly quickly, I'd sauce it at this point, but as it's going to be eaten throughout the week, I'll leave it 'dry' and dress it as I go. (Dry is a relative term - it's pretty juicy, and there's a bit of broth that ended up in the bottom of my storage container to keep it moist - but depending on what I'm using it for I may add just a bit of water to the meat as I warm it back up.)