Preheat a grill to medium. Put the pork chops and bell peppers in a shallow dish; season with salt and pepper. Heat 2 tablespoons olive oil, the shallots and 1 teaspoon thyme in a medium saucepan over medium heat. Cook until the shallots are softened, 3 minutes. Whisk in the jam until dissolved. Remove from the heat. Whisk in the ketchup, soy sauce and a few ice cubes; stir until the ice melts and the glaze cools. Pour half of the mixture over the pork and peppers; let sit 5 minutes. Reserve the remaining glaze for brushing.
Grill the pork, brushing with some of the reserved glaze, until cooked through, about 8 minutes per side. Transfer to a plate, tent with foil and let rest 5 minutes. Meanwhile, grill the peppers, turning and brushing with more glaze, until blistered and tender, 10 minutes; transfer to the plate.
Peel, pit and slice the avocados; gently toss with the remaining 2 tablespoons olive oil, the lime juice, chives and the remaining 1 teaspoon thyme. Season with salt and pepper. Serve with the pork and peppers.