Preheat the oven to 400 degrees F. Pulse the butter, lemon zest and juice, garlic, thyme, paprika, 2 teaspoons salt and 1 tablespoon pepper in a food processor until smooth.
Put the chickens on a rimmed baking sheet. Loosen the skin on the breasts and legs with your fingers. Rub about three-quarters of the lemon-pepper butter under the skin, then rub the rest all over the chickens. Refrigerate, uncovered, 2 hours or up to 8 hours before roasting.
Tie the chicken legs together with twine and tuck the wings under the body; place breast-side up on a rack in a large roasting pan. Pour the wine into the pan and transfer to the oven; roast until the chickens are golden and crisp and a thermometer inserted into the thickest part of the thigh registers 170 degrees F, about 1 hour, 50 minutes. (Tent with foil if the skin browns too quickly.)
Let the chickens rest 10 minutes before portioning (see below). Season with salt.
Grab one of the legs with tongs and pull it away from the body; cut through the skin with kitchen shears.
Pull the leg out and back to pop the joint; remove the leg with the shears. Repeat on the other side.
Separate the drumsticks from the thighs with the shears.
Cut off the wings as close to the body as possible.
Insert the shears into the tail end of the chicken and cut along the breastbone.
Pull back one of the breasts and cut it off the backbone. Repeat on the other side.