Preheat oven to 300 degrees. Season pork with salt and pepper. Transfer to a roasting pan; cover with parchment and then foil. Roast until pork is tender but not falling apart, 5 to 6 hours. (A paring knife inserted into the center should meet little resistance.)
About 30 minutes before pork is finished roasting, heat charcoal grill to medium, piling coals on 1 side to set up direct and indirect heat zones. Set a drip pan under the grill grate in the indirect heat zone. Cover grill.
Soak 4 cups applewood chips (barbecue-store.com) in water for 30 minutes. Drain 2 cups wood (leave 2 cups in water); add to coals.
Once smoke develops, transfer pork to grill rack, and set over drip pan. Position open lid vent over pork. (This will direct the smoke and impart maximum flavor.)
Smoke pork for 45 minutes. Drain remaining 2 cups wood; add to coals. Smoke pork for 30 minutes more. Shred pork using a fork, and serve with sauces.
Smoked pork can be refrigerated for up to 3 days.