You could always go a spicy pork tinga route instead of a traditional pulled pork. I've done the below recipe from America's Test Kitchen a couple of times and really liked it. Very low carb, and you could always use sprouted wheat bread/rolls instead of tortillas if you really wanted to lower the carbs.
You can find other pork tinga recipes on the web. I've always wanted to try Rick Bayless' recipe.
k.
SERVES 4 TO 6
The trimmed pork should weigh about 1 1/2 pounds. Tinga is
traditionally served on tostadas (crisp fried corn tortillas), but you
can also use the meat in tacos and burritos or simply served over
rice. Make sure to buy tortillas made only with corn, lime, and
saltpreservatives will compromise quality. For tips on baking
tostadas, see How to Bake Tostadas (related). Our winning brand of
ready-made tostadas, Mission, is also an excellent choice. We prefer
the complex flavor of chipotle powder, but two minced canned chipotle
chiles can be used in its place. The pork can be prepared through step
1 and refrigerated in an airtight container for 2 days. The tostadas
can be made up to a day in advance and stored in an airtight
container.
INGREDIENTS
Tinga
2 pounds boneless pork butt , trimmed of excess fat and cut into
1-inch pieces (see note)
2 medium onions , 1 quartered and 1 chopped fine
5 medium garlic cloves , 3 peeled and smashed and 2 minced or pressed
through garlic press (about 2 teaspoons)
4 sprigs fresh thyme
table salt
2 tablespoons olive oil
1/2 teaspoon dried oregano
1 (14.5-ounce) can tomato sauce
1 tablespoon ground chipotle powder (see note)
2 bay leaves
Tostadas
3/4 cup vegetable oil
12 (6-inch) corn tortillas (see note)
table salt
Garnishes
queso fresco or feta cheese
fresh cilantro leaves
sour cream
Diced avocado
Lime wedges
INSTRUCTIONS
1. FOR THE TINGA: Bring pork, quartered onion, smashed garlic cloves,
thyme, 1 teaspoon salt, and 6 cups water to simmer in large saucepan
over medium-high heat, skimming off any foam that rises to surface.
Reduce heat to medium-low, partially cover, and cook until pork is
tender, 75 to 90 minutes. Drain pork, reserving 1 cup cooking liquid.
Discard onion, garlic, and thyme. Return pork to saucepan and, using
potato masher, mash until shredded into rough ½-inch pieces (see
Step-by-Step below); set aside.
2. Heat olive oil in 12-inch nonstick skillet over medium-high heat
until shimmering. Add shredded pork, chopped onion, and oregano; cook,
stirring often, until pork is well browned and crisp, 7 to 10 minutes.
Add minced garlic and cook until fragrant, about 30 seconds.
3. Stir in tomato sauce, chipotle powder, reserved pork cooking
liquid, and bay leaves; simmer until almost all liquid has evaporated,
5 to 7 minutes. Remove and discard bay leaves and season with salt to
taste.
4. TO FRY TOSTADAS: Heat vegetable oil in 8-inch heavy-bottomed
skillet over medium heat to 350 degrees. Using fork, poke center of
each tortilla 3 or 4 times (to prevent puffing and allow for even
cooking). Fry 1 at a time, holding metal potato masher in upright
position on top of tortilla to keep it submerged (see photo below),
until crisp and lightly browned, 45 to 60 seconds (no flipping is
necessary). Drain on paper towel-lined plate and season with salt to
taste. Repeat with remaining tortillas.
5. TO SERVE: Spoon small amount of shredded pork onto center of each
tostada and serve, passing garnishes separately.