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My only concern is the fat. A pork should puts out a lot of fat and juice. The juice is delicious, but the fat is too much.
I always do this in a smoker, but if I were to use DO for this I think this is how I would do it.
So, give the shoulder a good rub with a barbecue seasoning of your choice. A lot of people would add barbecue sauce or even Dr. Pepper to the pot. I might go wiith some barbecue sauce thinned way out with beer. Only about an inch of liquid up the sides of the shoulder though.
Put it on the coals for a temp of 225-250 and let it go. You'll have to replenish coals every 45 minutes or so.
Turn the shoulder every time you add coals. When the roast reaches 190 or so, take it out and let it rest well wrapped for an hour. Meanwhile defat the juice from the pot. Reserve the juice.
Shred up the pork. Two forks or by hand is traditional. Shortcuts include chunks in the stand mixer and use the dough hook on low. Or smaller chunks in a food processor with the PLASTIC blade (NO STEEL) for a few pulses. This tends to produce a fine shred though.
Now, add a little rub to the shreds, mix. Add some of the juice and a bit of cider vinegar. Maybe some hot sauce too. Taste. Keep adding this combo of flavors until the result is as you like it.
Serve on buns with barbecue sauce and coleslaw.