I am sure the 4 gallons of coolant a day is an exaggeration or you would see it coming out.
First lets see what is what.
Cooling system has no pressure in it when cold
So top up radiator and leave the cap off
no coolant should come out of rad cap opening
coolant level may should drop a bit, top it up again
If coolant does come out of the rad cap opening and continues to come out after you top it up then you do have a cracked head or blown head gasket, period, there is no other source of pressure except the cylinders.
You can do the glove test(use our search) to ID what cylinder has the problem.
Coolant in the oil or oil in the coolant "can" be a sign of a head problem, but head problem doesn't always show that way.
White sweet smelling exhaust "smoke" is a sign of head problem and also why you see no leaks on the ground, coolant is being steamed out the tail pipe.
OK, so it isn't a head problem.
While engine is warming up 2 or 3 minutes, and you have topped up rad, put rad cap back on.
Fill up overflow tank to the COLD mark, about 1/2 way on most tanks.
Now feel the upper rad hose, it should be cold, thermostat will not open until coolant in the engine gets to 185-190 degrees(takes about 5 minutes), then it will start to open and upper rad hose will start to get warm.
190-200degs is "normal" operating temp of any gasoline engine, coolant will have expanded a bit and there should be pressure in the system.
If there isn't then rad cap is bad and overflow tank should have some extra coolant in it.
If overflow tank ever bubbles you have air in the system, could just be from you not filling it up or could be from blown head gasket.
After truck is fully warmed up see if it starts to overheat again
You have the 2.3l Duratec engine, which unfortunately was designed for transverse mounting, so it has a coolant connection in the back of the engine that can leak,
You need to drop the transmission to get to it, that's the bad news, good news is you said you don't see any leaks.