In a large bowl, coat goat with curry powders, all-purpose seasoning, salt, cumin, allspice, and Worcestershire sauce. Let marinate for at least two hours at room temperature, up to overnight, covered in the refrigerator.
Heat oil in large Dutch oven over medium heat. Add in half of goat and sear on all sides, until well-browned. (Do not crowd the pan and watch the heat during this process and turn heat down if the spices start to burn.) Remove goat and set aside in another bowl.
Add onion and cook until tender and translucent, about 2-3 minutes, stirring constantly. Then add the white and light green onions, garlic, and ginger and cook until fragrant, about 1 minute. Stir in tomato paste.
Slowly stir in 3 cups chicken stock, scraping the browned bits on the bottom. Add in all goat. Increase heat and bring to a boil, then reduce heat to low and add in thyme and pepper. Cover with a tight-fitting lid and simmer until goat is tender and falling apart, about an hour and 45 minutes. Check occasionally to ensure the goat is submerged in the liquid. If not, add more chicken stock.
Once the goat is cooked and tender, remove any bones, thyme stems, and scotch bonnet pepper. Add in potatoes, cover again, and cook until fork tender, about 20 minutes. Garnish with dark green portions of green onions and serve immediately with rice and peas or plantains.