In a large bowl, whisk together the aji panca paste, garlic (finely grated or mashed), red wine vinegar, vegetable oil, ground cumin, dried oregano, kosher salt, and black pepper until smooth; reserve 0.25 cup of this marinade for basting.
Trim the beef heart of exterior fat, valves, and silverskin; cut into 1.25–1.5 inch pieces. Add to the bowl with the remaining marinade and toss to coat well. Cover and refrigerate 4–12 hours.
Bring a large pot of water to a boil. Add the russet potatoes and the corn and simmer until the potatoes are just tender and the kernels are heated through, 15–18 minutes. Drain, let cool until handleable, then slice the potatoes into 0.75-inch rounds.
If using wooden skewers, soak them in water for 30 minutes. Preheat a grill to high heat (450–500°F) and clean the grates.
Pour the reserved marinade into a small saucepan and bring to a simmer over medium heat; cook 5 minutes to make a safe basting sauce, then keep warm.
Thread the marinated pieces onto skewers, packing them snugly but without crowding. Let any excess marinade drip off.
Grill the rounds and ears over direct heat, turning once, until lightly charred, 4–6 minutes for the rounds and 8–10 minutes for the ears; move to a cooler side of the grill to keep warm.
Grill the skewers over direct heat, turning every 1–2 minutes and brushing with the basting sauce each turn, until browned outside and still slightly rosy in the center, 8–10 minutes.
Transfer the skewers to a platter, brush once more with basting sauce, and rest 2 minutes. Serve hot with limes for squeezing and with the rounds and ears alongside.