So it turns out that the problem may not be a head gasket, or at least, signs aren't pointing towards a head gasket failure.
All other head gasket failures I have seen result in large amounts of coolant in the oil pan, or all over the ground under the car.
Mine has neither. The oil is 100% free of coolant.
However, that doesn't change the fact that when I was driving, I heard a loud release of pressure and saw a large cloud of white smoke behind my car. When I opened the hood I saw brown/green fluid all over the underside of the hood and driver's side of the engine bay. I assumed that the brown fluid was oil.
Fast forward to yesterday:
My father in law comes over and we check out the car. Try to turn it over and amazingly it fires right up. We let it idle for a good 5 minutes and it was fine, no problems whatsoever. No coolant leaking, coolant level in the resevoir remaining stable, everything looked good.
FIL put the car in drive, held his foot on the brake, and then applied some throttle to put a load on the motor. It seemed to be working fine, until I noticed that it was starting to knock. He let his foot off the throttle and engine died.
It took about 5 minutes of sitting before the engine would fire again, and after it started, it idled just fine.
To say the least, we are really puzzled. There is definitely a problem, but I don't think it's a head gasket.
Father in law thinks that maybe the coolant system got superheated and blew steam out of a loose hose somewhere, and when that happened, it basically steamed oily residue off of the engine compartment, and that was the brown liquid that I saw dripping everywhere.
It sounds like a good idea to me, but I really don't want to get my hopes up. I thought I'd update this thread and see if anybody knew what might be going on, but otherwise, I plan on taking it to a local Ford dealership to see if they can service it.