You are correct. There is no sway bar, only electronic sway control. The only item in the tow package that improves towing capacity is the heavy-duty radiator. Its questionable as to how much the heavy-duty radiator really improves tow capacity under normal conditions. The tow package does not include upgraded suspension or brakes.I could be wrong, but the sway control isn't a sway bar but rather an electronic sensing system that works with the brakes, there isn't any extra hardware associated with it.
It doesn't make sense that the heavy-duty radiator alone more than doubles the towing capacity. Maybe towing up a long uphill grade at high ambient temperatures. Most likely the "stock" van can tow more than 1500 pounds under most conditions. Just keep an eye on water and transmission temperature and take appropriate action if it becomes necessary. There is the warranty issue but that may be a low risk.