2001 Ford Taurus External coolant leak

My son recently purchased a 2001 Ford Taurus SES 3.0L OHV. Wanting a fresh start for routine maintenance, we went about flushing and changing out all the fluids (trans service with new filter, oil change, drain and fill power steering pump, plugs and wires, new fuel filter, new brake fluid and coolant flush and fill.) Everything went smoothly until the coolant flush. That seems to have caused more harm than good. Initially the coolant was very dark and the resevoir was very filthy. No visable signs of water in either the oil or the trans fluid at change, and since the engine did not get hot or seem to use oil or trans fluid, and no noticable odor, it was assumed to be corrosion and we proceeded with a flush of the system. 1st was a chemical flush and then a fresh water flush. After the refill we noticed a leak under the car where the water pump sits. Trying to locate the leak was hard to see but did notice water around the lower radiator hose where it connects to the water pump. Thinking this was the source, we tightened the hose, refilled the reservoir and ran until reaching operating temp. Seemed to be fine until shutting of the car. The leak seemed worse but still from the same area, so the hose was replaced. Again filled reservoir and brought to operating temp and shut off. Now it appeared to leak while car was running and quite profusely when it was shut off (draining the coolant reservoir), but it was still hard to pin point the leak from above or below. I should mention no tell tell signs of leakage from the weep hole of the water pump or noticable play in the shaft. Ok, at this point confusion took over and decided to remove the alternator, idler pulley and the power steering pump for a better look. Again to no avail. Purchased a radiator pressure tester kit, thinking I could get the leak to show up under pressure, but the system held 16# for 20 minutes. I am now at a loss and not thinking clearly. To wit, I have now pulled the thermostat to open a loop in the system, thinking that the system might not be full of water to allow the leak to show, of which, thinking a little clearer now, I realize that should not have made a difference in regards to the leak down pressure test. I should note though, that no water did come out of upper radiator hose and the engine via the thermostat removal. The thermostat did appear to be covered in a creamy coffee color slim as well as the housing. I'm thinking possibly the previous owners used a stop leak compound of some kind causing this appearance of sludge. What are your thoughts? Is there anything else I should do or can check while I have all the parts off. Could it possibly be the water pump gasket failing when the engine gets hot and expands? Should I just replace it now while it's accessible? Also, is there a way to bleed air from the system to ensure it is full of water? Can this be accomplished with the pressure tester somehow or am I just creating trapped air in the system by the pressure going out in all directions through the hoses connected to the reservoir? Sorry if I rambled on. I am so frustrated at this point, please help me get some logic back in my thought process. Maybe I just need to put everything back and start from square one. Any help you can provide will be greatly appreciated. As you probably can tell, I'm a novice shad tree mechanic, limited to the usual maintenance and part replacements. I will gladly triple my donation for a happy ending to this pain and misery. LOL