I'm pretty sure the flight to KHI is via BKK and I know the flight to CMB is via either Singapore or BKK. If you're looking for nonstops, your only options are BOM and DEL. And because of your mileage requirement, it looks like BOM is your option. But, I think you'd need a Visa for India, though I have no idea what the cost is. For US citizens, though, it's pretty high.