I picked up a 1998 Firebird with a V6 3.8L engine. 110,000 miles with an automatic. About 1 quart of antifreeze disappears with every 1/2 hr of driving until it loosed enough antifreeze to start overheating (about a gallon). So I refilled it while it was running, until full, put on the radiator cap and let is sit till the next day. I pressure tested it and it held 15 psig for 10 minutes (cold engine) and the it held rock steady - nothing leaking externally. Checked the oil an no antifreeze in the oil (no milk shake or discoloring). Removed all six plugs. they were all dark brown with some oil residue and all look identical (nothing washed out - just burning rich) - put in new plugs. Did a CO2 radiator test. Fluid stood blue, so no CO2 in the cooling system. No fog coming out of the tail pipes. When it warms up all of the condensate disappears (about 7 minutes) exhaust is clear. Does have an odd odder (not rotten eggs - jut potent that you got to walk away or choke) from the exhaust. Ran the gas down to about an 1/8 tank and filled up with regular. The odd odder did not go away. Someone did replace the cat with a piece of straight pipe. Car idles fine and runs fine and is responsive, for what it is. Removed the throttle body, cleaned out the antifreeze passage and installed a new gasket, and used high tack - no difference. Checked the over flow container and no increase in the antifreeze level. Put on a new OEM radiator cap for the heck of it. Replaced the radiator over flow hose - no difference. Radiator core is bypassed with a 180 hose bend on the engine. So where's the antifreeze going? What am I overlooking?
A half gallon of antifreeze an hour is a pretty substantial rate. There should be evidence. Did you fully bleed the system? Your cooling system typically takes 3-5 gallons of coolant. If the system is holding pressure fine, you've probably got air in the system.
One other thing that comes to mind is the water pump.
Sounds like you have checked it pretty well, but they can leak externally when going bad, and sometimes internally, I think on some fords.
It's either leaking coolant, or burning it. No other choices. Did you mean you bypassed the heater core? If so, I'd agree with @justin-shepherd that you may have had a large air gap in the system. I would also do a compression test just for quality.