If you eat a lizard’s brain while turning to stone, it cures your stoning.

There should be a way to remove confusion from pets. One simple way to accomplish this would be giving you a way to directly feed a lizard corpse to your pet, by making pets prioritize eating a lizard corpse when confused. Though this would not work for herbivorous or inediate pets.

Lizard corpses should go tainted like any other corpse, though they will still never rot away completely.

Lizards and cockatrices/chickatrices should grudge each other.

Sharply cut the frequency of lizards spawning (possibly even lower than 1/7), and possibly remove the special case that makes them always leave a corpse. This is because a player will usually accumulate enough of their corpses to be easily safe from any delayed stoning effect for the whole game. This won’t much affect reverse genociding them, if the player really wants a lizard corpse.

Also, possibly elevate their monster difficulty to something higher than 6; not because they are that difficult, but to make them appear only later on in the dungeon.

Alternatively, simply make lizard corpses rot, so that a player who wants to carry around a stoning defense must use other items, such as tins of lizard or acidic monsters, or potions of acid.

Lizard scales, available as a drop from killing a lizard, are wearable as AC 1 body armor. They can be upgraded into lizard scale mail, which has AC 3. This armor protects you from petrification.