I just went thru something similar on my daughter's neon. New radiator, 2 different stats , new cooling fans, new water pump and timing belt , etc etc

No leaks anywhere, Yet it would use about a half-gallon of coolant per day on 50 mile round trip. Took a bore scope and ckd combustion chamber and no issues found.
SO,,,,,

Finally I pulled the head suspecting gasket issue. Tops of the pistons were normal with no signs of burning coolant, no signs of a bad gasket. but. Ckd the head for cracks ( found none ) put a new gasket and head bolts on it. And hasn't been a problem since