4mA is fine, won't trip the standard 30mA gfci we use here but ground path should be low impedance and meassure pretty close to neutral or the pipe. Also, measuring current in such conditions is kind of dangerous, if it were correctly conncected the current could blow at least the fuses if you have a proper scope like the 87V.
To solve this I keep my mind with using the pipes, is not new to do so. Many structural parts are used as ground and pipes are usually the easier to get to. Avoid gas pipes and try to disconnect from the outside as all your neighbours in the buildong dumping the leakage to your installation isn't nice either.
I've tried to replace an structural ground with a proper one in an industrial enviroment, the structural one showed 10Ω being a tad high for an industrial installation. A 3m rod measured well over 100Ω because a really crappy dirt, kind of sand... So I would need 20 of those rods to get it better, no deal, took the rod out (you would normally leave it there but we had the elevator). Luckily there was an unused train rail right next to the building, less than a meter away, so there was my better grounding measuring less than 3Ω but measurements are kind of hard to get as the dirt, as said, is crap.
JS