Although it's going to be harder to see anything since you report it isn't doing it in park, you might want to pop the hood and see if you can detect any excessive wobble in anything, the belt tensioner (or just loose belt), water pump, AC, alternator, steering pump, though if water or steering are that bad they're probably leaking fast too... but you did report overheating and needing to add water. Where is your water loss coming from? Edit: Never mind, I see in another topic you had a radiator leak.
I wonder if recording the sound and posting it on youtube would help someone identify it.
I assume you're using the right spark plug heat range, don't have dodgy poor fuel in it, aren't using detergent free oil, no vacuum leaks (no lean or other engine trouble codes set?) nor anything else that could contribute to predetonation knock, but if that is what is happening, it's no surprise it would happen worse with an overheating engine.
Just for the heck of it you might see if topping off the tank with premium fuel helps. It's about the cheapest/easiest thing to do to narrow down if it's predetonation.
I'm not sure if your generation of V8 has a knock sensor but I was led to believe it didn't. There could instead be more serious problems like internal wear. How many miles on it? How long was it overheating?