Hair dryer. Period. I've tried everything else, and nothing works as consistently. Point the dryer, on medium heat, at the edge of the elements (with the front ring removed - BTW, when removing the ring, loosen the screws without removing them, 'cause they're impossible to get restarted, and made of easily-stripped aluminum). Move the heat around so you gently and evenly heat the parts. Use a towel to unscrew. Never takes me more than about 30 seconds or so of heating.
When all the stuck parts are separated, you must remove all of the old grease before relubing with an appropriate grease. I use a small brass brush dipped in Goof-Off (essentially xylene) for this step, and relube with Teflon grease thinned a little with Rem Oil.