I do pulled pork like that. Looking for 190 internal temp at which point I wrap it in foil, then newspaper, then a towel and put it in a cooler for a while before pulling.
Takes it from tender to melt in your mouth.
I usually just shot off the oven, and let it cool down in there until I’m ready to deal with it. Given the long cook time, this usually means making it one day and starting to eat it the next, but that gives more time for the pork to absorb the flavors from the sauce. (We tend to also cook chili in advance because the flavor intensifies if you store it in the fridge for a day, and it reheats very well.)