Prepared in 45 minutes or less.
For the Chicken:
Discard any visible fat from chickens. Rinse chickens and pat dry.
Put 1 chicken, breast up, on a cutting board. Pull 1 leg away from body and with a sharp knife cut through skin between leg and breast until you hit joint (do not cut through joint). With your fingers behind joint, bend leg back until joint pops.
Repeat with other leg. With kitchen shears, cut through rib bones (starting from thigh) on both sides of breast up to, but not through, shoulder joints. Open chicken, skin side up. Press on breastbone to crack and flatten with heel of your hand. Repeat with second chicken.
For the Marinade:
Purée garlic with ¼ cup oil, paprika, oregano, cumin, allspice, 2 Tbsp salt (preferably fine sea salt), and 2 tsps pepper in a blender or food processor until smooth.
Stir together 1 tbs marinade and remaining 2 tbs oil in a small bowl and reserve, chilled, for basting.
Put chickens in a large 4-sided sheet pan. Using a few lemon slices as spreaders, rub some of marinade all over chickens, then stuff lemon slices with remaining marinade under skin of breasts and thighs. Marinate, chilled, at least 8 hours (and up to 12).
Prepare grill for indirect-heat cooking over medium-hot. Oil grill rack, then grill chickens directly over coals, turning once, approximately 5 minutes or until browned. Be careful of flame flare-ups. Move chickens to area of grill with no coals underneath and grill, covered, turning occasionally and basting with reserved marinade mixture, until chickens are cooked through, 40 to 45 minutes. Discard any leftover basting sauce.
Add more charcoal as necessary. Allow to stand 10 minutes before cutting into serving pieces. Serve on large platters garnished with fresh lemon wedges.