On April 20, all petrifying attacks of monsters have the same effects they do on a new moon, i.e. making stoning more likely.

There should be some special effect, even just an acknowledging message, when trying to apply a mirror to a cockatrice, since the encyclopedia mentions its own reflection is fatal to it and the materials to make it look at its reflection exist in the game.

When polymorphed into a form that has automatic bite or other melee-touching attack, if you are about to attack a cockatrice, make it subject to an Intelligence saving throw; if you pass this you avoid attacking the monster with your body.

Lizards and cockatrices/chickatrices should grudge each other.

If you deliver a staggering blow or other knockback to a cockatrice, and there is a monster behind it, that monster might get stoned.

Petrification sources need to be made more consistent - logically, “The cockatrice touches you!” should have the same effect as touching its corpse, but instead it is a mere 1/30 chance of starting a delayed petrification.

Deafness should provide total protection against cockatrices’ hissing attacks.

Deafness protects against cockatrice hissing and therefore their stoning. (This might be too powerful; it might need to just reduce the chance of stoning rather than eliminating it altogether.)

If you hit a cockatrice with a corpse of a non-petrification-resistant monster, the corpse turns into a statue.