I'm afraid theres not much you can do. With respects to RFI/EMI its an 18 inch antena and theres no changing that. The larger the coil, the more of that it will pick up. The carbon based shielding used on Explorer coils is not an effective shield against RFI/EMI, it just shields against static and ground capacitance.
If the stability issues are due to ground mineralization again its biting off an 18 inch size chunk of ground, quite a bit more than the stock coil. You could reduce your sensitivity and gain but then you lose depth, which is probably the reason one would swing a coil that large in the first place.
If the stability is just rediculous regardless of settings you might have a bad coil. Try swinging it a couple inches off the ground without touching the grass, does it sound stable? If so now let it brush across the grass or ground, if it goes nuts it might be bad. You can alternatively yank out a clump of grass and brush the grass over the coil at various spots, you may find a weak spot in the shielding somewhere where it falses when you brush the grass across it.