Heat oven to 475°. Season cavities and outsides of hens with salt and pepper; stuff rosemary and thyme into cavities and tie legs together using butchers' string.
Heat bacon and 1 tbsp. butter in a 12" skillet over medium; cook until bacon is slightly crisp, 18–20 minutes.
Using a slotted spoon, transfer bacon to a roasting pan.
Add garlic, onions, salt, and pepper to skillet and toss in fat; add to roasting pan.
Add oil to skillet and, working in batches, cook hens, turning as needed, until browned, 10–12 minutes; set hens breast-side up in roasting pan.
Add shallot to skillet; cook until soft, 3–4 minutes.
Add juice; cook until slightly reduced, 3–4 minutes.
Stir in kumquats, honey, paprika, salt, and pepper; simmer until thickened, 12–15 minutes.
Stir in remaining butter.
Brush half the sauce over hens; keep remaining sauce warm.
Roast hens, basting often with pan juices, until an instant-read thermometer inserted into the thickest part of the thigh reads 165°, about 45 minutes.
Transfer hens, bacon, garlic, and onions to a serving platter; spoon remaining sauce over the top.
