I personally wouldn't use EEZOX.
It has chlorinated esters in it, and chlorinated esters - even tiny amounts can cause Chloride Stress Corrosion Cracking, especially in stainless steel.
EEZOX claims that the amout of chlorinated ester in their cleaning solution is so low that it won't negatively affect the metal in guns, but IMO, there are enough alternative cleaners and lubes out there that are chlorine free that I'd much rather use those.