In a small bowl, combine allspice, thyme, salt and pepper. Set aside 1/2 teaspoon. Stir into the remaining spices the lime juice, 1 tablespoon of the oil, the garlic and hot sauce. Place pork in a resealable plastic bag and spoon in the spice and lime juice mixture. Shake to coat pork with mixture. Refrigerate for 6 to 8 hours.
Heat remaining 1 tablespoon oil in a large nonstick skillet over medium-high heat; add pork and cook 12 to 14 minutes, until internal temperature reaches 140 degrees F, turning so all sides brown. Remove to a plate.
Heat a lightly greased stovetop grill pan and grill the polenta slices about 5 minutes, turning once.
Heat stewed tomatoes and stir in reserved 1/2 teaspoon seasoning mix.
Slice pork and serve over a bed of spinach, if desired, with the grilled polenta and stewed tomatoes.