The high prices work to incentivize competitors to enter the market and increase the supply. If only the government would stop letting competitors merge together...
No, the alternative to price gouging is to maintain a normal profit margin since your flocks didn't have to be culled and your costs have not gone up.
If anything, the flocks that had to be culled would have caused a sudden chicken feed surplus and their feed cost should have fallen.
If there are fewer eggs, then there are fewer eggs. The only thing left to discuss is who has the right to obtain them, and who will not. Usually, society accepts that people with more money get more access to things than people with less money.
Colluding to price gouge consumers when costs have not increased is illegal behavior.