I'm posting this observation just FYI in case it might be useful to someone.
After I built my electric stove (rebuilt using parts from a drop-in range top - see the Stovezilla thread) I had a problem - every time I turned on one or more elements, the GFCI would trip - sometimes it would work for a minute or so, then sometimes drop out as soon as I turned on a coil. I decided to disable the GFCI temporarily and see how long it would take to boil 8 gallons of water - during this test I had the burners on high for 48 minutes and then on a somewhat lower level for about 30 minutes. The next day, I re-enabled the GFCI and found that the stove would stay on without tripping the GFCI.
I though maybe there was some baked on grease providing a conductive path and that this had gotten burned off during the boil test. I measured the current flowing in the ground wire and noticed that one coil seemed to have more current flowing to ground than the other and when I swapped that coil with another, the problem followed the coil. So I bought a replacement coil to have as a spare, just in case one of the old ones failed. When I tried the new one, after a minute or so, it tripped the GFCI, so it wasn't a grease problem. I disabled the GFCI again and ran the new coil on high for about 10 minutes, then re-enabled the GFCI and now the new coil worked OK.
Watching the ground current, as soon as I turn on a cold coil, the current gradually increases as the coil heats, reaching a level of maybe 0.05 or 0.1 milliamps on the "good" coils. If the control knob is on a setting less than "high", as soon as the bi-metal strip in the control turns off power to the coil, the ground current increases to about 0.5 to 0.7 milliamps on the "good" coils, then drops back to the lower value when the control switches the coil back on. On the "bad coils", the ground current must be more than the approximately 5 mA required to trip the GFCI.
Conclusions: There is a conductive path in all these elements (the original stove is a Whirlpool, and the new coil I bought is a 1500 watt element from Lowe's). The conductive path is not old grease, but I suspect it may be moisture which gets inside the coil into the insulation that insulates the heating wire from the outer sheath. Heating the coil eventually drives this moisture off (how it gets out I don't know). It's interesting that the ground current is near zero when the control has cycled power onto the coil. This implies a conductive path which is either in the center of the coil length, or symmetrically spread out around the center (equal current into and out of ground). Of course, the ground current increases when the control cycles the power off, because in this situation, one end of the coil is open circuited and the entire coil is at 120 volts w.r.t. ground. With a single randomly located "bad" spot, I'd expect more than the near zero ground current during the "on" portion of the cycle.
So if you are trying to use one of these coil elements with a GFCI and the GFCI is tripping for some unknown reason, try baking the coil for a while to see if that solves the problem.