In a small bowl, combine the garlic, brown sugar, lime peel, lime juice, mustard and 1 teaspoon each salt and pepper. Arrange the ribs in a casserole dish and rub with the marinade; cover and refrigerate for at least 4 hours or overnight.
Preheat a grill or grill pan to medium-high. In a medium pot, combine the potatoes and enough salted water to cover. Bring to a boil, then lower the heat and simmer until tender, 15 to 20 minutes; drain and transfer to a medium bowl. Smash the potatoes with the back of a fork; season with salt and pepper. Cover and keep warm.
Meanwhile, season the zucchini with salt and pepper and grill cut side down, turning halfway through, until softened, 10 to 15 minutes.
Grill the ribs, basting with the marinade and turning occasionally, for 10 minutes. Discard the remaining marinade and continue grilling the ribs until well browned, about 10 minutes more. Transfer to a platter and tent with foil.
Stuff the zucchini with the smashed potatoes and top with the salsa; serve with the ribs.