Remove the papery skin from the back of each rack of ribs; place the ribs in a roasting pan.
Combine the garlic, thyme, oregano, marjoram, salt, cinnamon stick, allspice berries, cloves, vinegar, and 3 tablespoons water in a blender or spice mill; process to a smooth paste, adding more water, if needed.
Rub this paste over the ribs on both sides, cover, and let marinate, in the refrigerator, at least overnight and up to 24 hours.
Preheat grill to medium; when ready to cook, season the ribs with salt; oil the grill grate, then arrange the ribs on the hot grate, meaty side down.
Grill the ribs until nicely browned and cooked through, 30-40 minutes in all, turning once or twice with tongs.
Cut the racks into sections of 2 or 4 ribs for serving; serve with Salsa Mexicana.
To make the salsa--cut tomatoes, onion, and chiles into 1/4-inch dice (you can soften the bite of the chiles by scraping out the veins and seeds); combine in a serving bowl.
Add in cilantro, lime juice, and salt; toss to mix; adjust seasoning to taste by adding more lime juice or salt.