Toss pork and 1 ½ teaspoons salt together in a bowl; refrigerate for 1 hour.
Combine New Mexican chiles and 4 cups boiling water in medium bowl. Cover and let sit until chiles are softened, about 30 minutes. Adjust oven rack to lower-middle position and heat oven to 325ºF (162ºC) degrees.
Drain chiles, reserving 2 cups soaking liquid. Process chiles, honey, vinegar, garlic, oregano, cumin, cayenne, cloves, and ½ teaspoon salt in a blender to a thick paste, about 30 seconds.
With blender running, slowly add reserved soaking liquid and blend until smooth, about 3 minutes.
Combine pork and chile sauce in Dutch oven, stirring to coat, then bring to a boil over high heat. Cover pot, transfer to oven, and cook until pork is tender and fork inserted into pork meets little resistance, 2 to 2½ hours.
Using wooden spoon or rubber spatula, scrape any browned bits from sides of pot and stir into pork until sauce is smooth and homogenous. Let stand, uncovered, for 10 minutes. Season with salt to taste. Serve with lime wedges.