Hi Kevin, Maybe I can shed some light. My first smoker was a charcoal Brinkman vertical as you have. Very unreliable for a heat source. Every time you open it to mop, you lose all the heat. Even keeping it shut, it has a tendency to cool off quickly. Also suffers from different temps at different levels. Having said that, the best way to really know if a piece of meat is ready, is by temperature. And since getting an accurate read is difficult, especially with bone-in items, then a dual probe thermometer is best. Try to make sure the probes are inserted in a meat , not near the bone. I will also point out, if you really cooked a 6 lb shoulder that length of time at the constant temp of 225, you would easily have reached temp. internal of 195 deg, all you need. Your problem is the smoker, and opening the smoker. When I had my brinkman, I drilled holes at 3 levels, one at the water pan, one at grill level and one on top of the dome. and mounted round dial thermometers, (cheap at Lowes) I would see a 30 degree difference sometimes from middle to top. So I mounted a couple brackets, and lowered a rack to just 2 inches above the water pan.
Now lets talk meat. Butt, Shoulder, Picnic, all can be used for pulled pork, Bone in is preffered IMO, moister end results. Look for a cut with a nice fat cap. Look for one with fat marbeling if possible. Almost ALL pork products in the California area are Smithfield or Farmer John. I have used both, with always great results. Winco, Safeway, Smart and Final, Sams Club, Costco, Food Maxx, Vons, Ralphs, Lucky, Nobb Hills, all buy their pork products from the same master distributors. Period. I know, I was a butcher. Of course, you can get a lousy cut from anybody. It is up to you to check expiration dates and inspect for fat etc. But other than HOW the butcher trimmed it, it came from the same wholesale distributors. Inferior pork products go to commercial users, hot dogs, breakfast sausage, institutions, canners etc. Grocers all use top grade.
Since the Brinkmann has such temp issues, I solved it as I said above, but also realized that in 5 hours of smoking I had imparted enough smoke flavor by fat into my meat. So I would take my meat, wrap in foil and finish it in the oven for 2 or so hours at 250. (remember , it is not the time, it is the internal temp or 195 you need.) This method helps retain some moisture, yet still has plenty of smoke flavor. I hope this all help you, pulled pork is really easy when done correctly, it needs no baby sitting really. The fat cap will baste your beat as it cooks, no need to mop so much either.
Big Rich Morris